Question

If amp $\left(z_1{z}_2\right)=0$ and $|z_1|=|z_2|=1$, then

• A. $z_1+z_2=0$
• B. $z_1{z}_2=1$
• C. $z_1={\overline{z}}_2$
• D. none of these

Answer 1

Answer: (B), (C)

The correct options are
B $z_1={\overline{z}}_2$
C $z_1{z}_2=1$

Let $z_1=e^{ia}$
Then
$z_2=e^{-ia}$ ...since $arg(z_1.z_2)=0$
Hence
$\Rightarrow z_2=\overline{z_1}$
Or
$\Rightarrow z_1=\overline{z_2}$
And
$\Rightarrow z_1.z_2$
$=e^{i0}$
$=1$