Question

Find all complex numbers $z$ which satisfy the following equation:

$z=\overline{z}$

• A. $x=0$
• B. $y=0$
• C. $z=0$
• D. $x=0,y=0$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $y=0$
C $z=0$
D $x=0,y=0$

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

Now it is given that, $z=\overline{z}$

$\Rightarrow x+iy=x-iy$

Equating the coefficients we get, $x=x$ and $y=-y\Rightarrow y=0$

Hence $z=x\in R$

Thus the solution is all the point lying on the real axis.

Hence, options B, C and D are correct.