Is this a pure imaginary number or real number?











up vote
3
down vote

favorite












Is $dfrac{0}{2yi}$ a pure imaginary number or a real number?



I'm debating, $0$ is a real number but if you divide by $i$, it's imaginary.










share|cite|improve this question









New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    isnt that number just $0$?
    – Jorge Fernández
    6 hours ago










  • Hi, and welcome to MSE. This is a great help on here: math.meta.stackexchange.com/questions/5020 Look what I did to your post! Click edit and you can see the MathJax that does this.
    – Robert Frost
    5 hours ago












  • You left out another possibility: when $y=0$, the expression is undefined.
    – amd
    4 hours ago















up vote
3
down vote

favorite












Is $dfrac{0}{2yi}$ a pure imaginary number or a real number?



I'm debating, $0$ is a real number but if you divide by $i$, it's imaginary.










share|cite|improve this question









New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
















  • 1




    isnt that number just $0$?
    – Jorge Fernández
    6 hours ago










  • Hi, and welcome to MSE. This is a great help on here: math.meta.stackexchange.com/questions/5020 Look what I did to your post! Click edit and you can see the MathJax that does this.
    – Robert Frost
    5 hours ago












  • You left out another possibility: when $y=0$, the expression is undefined.
    – amd
    4 hours ago













up vote
3
down vote

favorite









up vote
3
down vote

favorite











Is $dfrac{0}{2yi}$ a pure imaginary number or a real number?



I'm debating, $0$ is a real number but if you divide by $i$, it's imaginary.










share|cite|improve this question









New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Is $dfrac{0}{2yi}$ a pure imaginary number or a real number?



I'm debating, $0$ is a real number but if you divide by $i$, it's imaginary.







complex-numbers






share|cite|improve this question









New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 5 hours ago









Robert Frost

4,1961039




4,1961039






New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 6 hours ago









Maske13

161




161




New contributor




Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 1




    isnt that number just $0$?
    – Jorge Fernández
    6 hours ago










  • Hi, and welcome to MSE. This is a great help on here: math.meta.stackexchange.com/questions/5020 Look what I did to your post! Click edit and you can see the MathJax that does this.
    – Robert Frost
    5 hours ago












  • You left out another possibility: when $y=0$, the expression is undefined.
    – amd
    4 hours ago














  • 1




    isnt that number just $0$?
    – Jorge Fernández
    6 hours ago










  • Hi, and welcome to MSE. This is a great help on here: math.meta.stackexchange.com/questions/5020 Look what I did to your post! Click edit and you can see the MathJax that does this.
    – Robert Frost
    5 hours ago












  • You left out another possibility: when $y=0$, the expression is undefined.
    – amd
    4 hours ago








1




1




isnt that number just $0$?
– Jorge Fernández
6 hours ago




isnt that number just $0$?
– Jorge Fernández
6 hours ago












Hi, and welcome to MSE. This is a great help on here: math.meta.stackexchange.com/questions/5020 Look what I did to your post! Click edit and you can see the MathJax that does this.
– Robert Frost
5 hours ago






Hi, and welcome to MSE. This is a great help on here: math.meta.stackexchange.com/questions/5020 Look what I did to your post! Click edit and you can see the MathJax that does this.
– Robert Frost
5 hours ago














You left out another possibility: when $y=0$, the expression is undefined.
– amd
4 hours ago




You left out another possibility: when $y=0$, the expression is undefined.
– amd
4 hours ago










4 Answers
4






active

oldest

votes

















up vote
3
down vote













You told us nothing about $y$ but, assuming that $y$ is a non-zero complex number, then $dfrac0{2yi}=0$, which is both a real number and a pure imaginary number. It's actually the only complex number with both properties.






share|cite|improve this answer




























    up vote
    2
    down vote













    We have that



    $$frac{0}{2yi}=0$$



    which is an integer, a rational, a real and a complex number.



    Notably it indicates the neutral element with respect to addition.






    share|cite|improve this answer





















    • ...and the absorbing element under multiplication.
      – Robert Frost
      5 hours ago


















    up vote
    1
    down vote













    If $yneq 0$, in the complex plane, by definition, $0=0+0i$. Since the imaginary and real parts are 0, 0 is purely real and imaginary. However, it's also member of the complex numbers.






    share|cite|improve this answer




























      up vote
      1
      down vote













      $0$ being purely real and purely imaginary need not be more surprising than, as a real number, it is neither positive nor negative.






      share|cite|improve this answer





















      • This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
        – max_zorn
        4 hours ago











      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });






      Maske13 is a new contributor. Be nice, and check out our Code of Conduct.










      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3020734%2fis-this-a-pure-imaginary-number-or-real-number%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      4 Answers
      4






      active

      oldest

      votes








      4 Answers
      4






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      3
      down vote













      You told us nothing about $y$ but, assuming that $y$ is a non-zero complex number, then $dfrac0{2yi}=0$, which is both a real number and a pure imaginary number. It's actually the only complex number with both properties.






      share|cite|improve this answer

























        up vote
        3
        down vote













        You told us nothing about $y$ but, assuming that $y$ is a non-zero complex number, then $dfrac0{2yi}=0$, which is both a real number and a pure imaginary number. It's actually the only complex number with both properties.






        share|cite|improve this answer























          up vote
          3
          down vote










          up vote
          3
          down vote









          You told us nothing about $y$ but, assuming that $y$ is a non-zero complex number, then $dfrac0{2yi}=0$, which is both a real number and a pure imaginary number. It's actually the only complex number with both properties.






          share|cite|improve this answer












          You told us nothing about $y$ but, assuming that $y$ is a non-zero complex number, then $dfrac0{2yi}=0$, which is both a real number and a pure imaginary number. It's actually the only complex number with both properties.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 6 hours ago









          José Carlos Santos

          142k20112208




          142k20112208






















              up vote
              2
              down vote













              We have that



              $$frac{0}{2yi}=0$$



              which is an integer, a rational, a real and a complex number.



              Notably it indicates the neutral element with respect to addition.






              share|cite|improve this answer





















              • ...and the absorbing element under multiplication.
                – Robert Frost
                5 hours ago















              up vote
              2
              down vote













              We have that



              $$frac{0}{2yi}=0$$



              which is an integer, a rational, a real and a complex number.



              Notably it indicates the neutral element with respect to addition.






              share|cite|improve this answer





















              • ...and the absorbing element under multiplication.
                – Robert Frost
                5 hours ago













              up vote
              2
              down vote










              up vote
              2
              down vote









              We have that



              $$frac{0}{2yi}=0$$



              which is an integer, a rational, a real and a complex number.



              Notably it indicates the neutral element with respect to addition.






              share|cite|improve this answer












              We have that



              $$frac{0}{2yi}=0$$



              which is an integer, a rational, a real and a complex number.



              Notably it indicates the neutral element with respect to addition.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered 6 hours ago









              gimusi

              88.5k74394




              88.5k74394












              • ...and the absorbing element under multiplication.
                – Robert Frost
                5 hours ago


















              • ...and the absorbing element under multiplication.
                – Robert Frost
                5 hours ago
















              ...and the absorbing element under multiplication.
              – Robert Frost
              5 hours ago




              ...and the absorbing element under multiplication.
              – Robert Frost
              5 hours ago










              up vote
              1
              down vote













              If $yneq 0$, in the complex plane, by definition, $0=0+0i$. Since the imaginary and real parts are 0, 0 is purely real and imaginary. However, it's also member of the complex numbers.






              share|cite|improve this answer

























                up vote
                1
                down vote













                If $yneq 0$, in the complex plane, by definition, $0=0+0i$. Since the imaginary and real parts are 0, 0 is purely real and imaginary. However, it's also member of the complex numbers.






                share|cite|improve this answer























                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  If $yneq 0$, in the complex plane, by definition, $0=0+0i$. Since the imaginary and real parts are 0, 0 is purely real and imaginary. However, it's also member of the complex numbers.






                  share|cite|improve this answer












                  If $yneq 0$, in the complex plane, by definition, $0=0+0i$. Since the imaginary and real parts are 0, 0 is purely real and imaginary. However, it's also member of the complex numbers.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 6 hours ago









                  Alex R.

                  24.6k12352




                  24.6k12352






















                      up vote
                      1
                      down vote













                      $0$ being purely real and purely imaginary need not be more surprising than, as a real number, it is neither positive nor negative.






                      share|cite|improve this answer





















                      • This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
                        – max_zorn
                        4 hours ago















                      up vote
                      1
                      down vote













                      $0$ being purely real and purely imaginary need not be more surprising than, as a real number, it is neither positive nor negative.






                      share|cite|improve this answer





















                      • This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
                        – max_zorn
                        4 hours ago













                      up vote
                      1
                      down vote










                      up vote
                      1
                      down vote









                      $0$ being purely real and purely imaginary need not be more surprising than, as a real number, it is neither positive nor negative.






                      share|cite|improve this answer












                      $0$ being purely real and purely imaginary need not be more surprising than, as a real number, it is neither positive nor negative.







                      share|cite|improve this answer












                      share|cite|improve this answer



                      share|cite|improve this answer










                      answered 5 hours ago









                      badjohn

                      4,2101620




                      4,2101620












                      • This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
                        – max_zorn
                        4 hours ago


















                      • This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
                        – max_zorn
                        4 hours ago
















                      This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
                      – max_zorn
                      4 hours ago




                      This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review
                      – max_zorn
                      4 hours ago










                      Maske13 is a new contributor. Be nice, and check out our Code of Conduct.










                      draft saved

                      draft discarded


















                      Maske13 is a new contributor. Be nice, and check out our Code of Conduct.













                      Maske13 is a new contributor. Be nice, and check out our Code of Conduct.












                      Maske13 is a new contributor. Be nice, and check out our Code of Conduct.
















                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.





                      Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                      Please pay close attention to the following guidance:


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3020734%2fis-this-a-pure-imaginary-number-or-real-number%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      Popular posts from this blog

                      Contact image not getting when fetch all contact list from iPhone by CNContact

                      count number of partitions of a set with n elements into k subsets

                      A CLEAN and SIMPLE way to add appendices to Table of Contents and bookmarks