Is this a pure imaginary number or real number?











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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







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  • 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.






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.
















  • 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.






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.











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




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









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Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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share|cite|improve this question




share|cite|improve this question








edited 5 hours ago









Robert Frost

4,1961039




4,1961039






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asked 6 hours ago









Maske13

161




161




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Maske13 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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  • 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
        5 hours ago











      Your Answer





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      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
                        5 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
                        5 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 6 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
                        5 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
                        5 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
                      5 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
                      5 hours ago










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