Question

If z is a complex number, then z.$\overline{z}$ = 0 if and only if

• A. z=0
• B. Re(z)=0
• C. Im(z)=0
• D. None of these

Answer 1

The correct option is A

z=0

Let z = x+iy, $\overline{z}$ = x-iy

∴ z$\overline{z}$ = 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