Question

Let z, $\omega$ be a complex numbers such that $\overline{z}+i\overline{\omega }=0$ and Arg z$\omega =\pi$ then arg. of z equals

• A. $\frac{3\pi }{4}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{5\pi }{4}$

Answer 1

The correct option is A $\frac{3\pi }{4}$

$\overline{z}+i\overline{\omega }=0$
$\Rightarrow \overline{z}=-i\overline{\omega }$
$\Rightarrow z=i\omega$
$\Rightarrow \omega =-iz$
$\therefore arg(-i{z}^2)=\pi$
$\Rightarrow arg(-i)+2arg\left(z\right)=\pi$ $\Rightarrow 2arg\left(z\right)=\pi +\pi /2=3\pi /2$
$\Rightarrow arg\left(z\right)=3\pi /4$