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Algebra Level 1

A number which is both purely real and purely imaginary is ... ?


The answer is 0.

Palash Som by Palash Som , 21, India

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4 solutions

Saatvik Jain
Feb 11, 2016

In the argand plane, the Y axis represents purely imaginary numbers and X, purely real. If we want a number that is both purely real and purely imaginary, we will have to find the point of intersection of these two axis, which indeed is the origin (0,0).

The number representing origin will be 0+0i = 0

Hope this helps.

14 Helpful 0 Interesting 0 Brilliant 0 Confused
Whitney Clark
Feb 11, 2016

Since zero is real, and real numbers are not imaginary, I'm not sure I agree with this.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i i .

0 × i = 0 0\times i=0

Thus, zero is in fact both a real number and an imaginary number. Another way is by looking at the complex plane (or Argand plane). All the points in the plane have a real part and an imaginary part. All the points in the real axis have the imaginary part 0 i = 0 0i=0 .

Kenneth Choo - 5 years, 2 months ago
Hamza A
Feb 5, 2016

a purely imaginary number is a number that lacks a real part,a purely real number is a number that lacks an imaginary part,zero can fit in both

see: complex numbers

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Firstly, the basic definition of an imaginary/complex number is that it is such a number which cannot be represented on a numberline. 0 can be represented on the number line

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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