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Question

If z is a complex number such that Rez=Imz, then


A

Rez2=0

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B

Imz2=0

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C

Rez2=Imz2

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D

Rez2=-Imz2

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E

z2=0

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Solution

The correct option is A

Rez2=0


Explanation for the correct option.

Find the real and imaginary part of z2.

Let z=x+iy be a complex number. Its real part is x and imaginary part is y.

It is given that Rez=Imz, so x=y.

Now find z2.

z2=x+iy2=x2+2x×(iy)+i2y2=x2+2xyi+(-1)x2i2=-1,x=y=x2+2xyi-x2=2xyi

So the complex number z2 is 2xyi. So its real part is 0, Rez2=0 and its imaginary part is 2xy, Imz2=2xy.

Hence, the correct option is A.


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