Question

If $z_1$, $z_2$are conjugate complex numbers and arg $\left(z_1{z}_2\right)=$

• A. $arg{z}_1+arg{z}_2=0$
• B. $arg{z}_1+arg{z}_2+n\pi$, $nϵ\{-1,0,1\}$
• C. $arg{z}_1+arg{z}_2+n\pi$, $nϵN$
• D. $arg{z}_1-arg{z}_2$

Answer 1

The correct option is A $arg{z}_1+arg{z}_2=0$

$z_1$ and $z_2$ are conjugates of each other.

Hence, $z_1{z}_2=|z_1{|}^2$

$z_1{z}_2$ is real and positive.

Hence, arg$\left(z_1{z}_2\right)=0$

Also, arg $z_1$ +arg $z_2=0$

Hence, option A is correct.