If z is a complex number, then z. ¯ z = 0 if and only if Options: A . &nbsp z=0 B . &nbsp Re(z)=0 C . &nbsp Im(z)=0 D . &nbsp None of these

If z is a complex number, then z.¯z = 0 if and onl

Question -

If z is a complex number, then z. $¯ z$ = 0 if and only if

Options:

A . z=0

B . Re(z)=0

C . Im(z)=0

D . None of these

Answer: Option A
:
A

Let z = x+iy, $¯ z$ = x-iy

∴ z $¯ z$ = 0 ⇒ (x+iy)(x-iy) = 0 ⇒ $x^{2} + y^{2}$ = 0

It is possible onle when x and y oth simultaneously zero

i.e, z = 0 +0i = 0

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