Question

If $Z$ and $W$ are two complex numbers such that $\overline{z}+i\overline{w}=0$ and $arg\left(zw\right)=\pi$ then $arg\left(Z\right)=$____________

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

Answer 1

Answer: (C)

$\frac{3\pi }{4}$

$\begin{array}{c}\overline{z}+i\overline{w}=0\\ Takingconjugate\\ z-iw=0\Rightarrow w=\frac{z}{i}\\ \left(zw\right)=\pi \\ \left(z\times \frac{z}{c}\right)=\pi \\ \left(\frac{z^2}{c}\right)=\pi \\ 2\left(z\right)-\left(i\right)=\pi \\ 2\left(z\right)-\frac{\pi }{2}=\pi \\ 2\left(z\right)=\pi +\frac{\pi }{2}\\ \left(z\right)=\frac{3\pi }{4}Ans.\end{array}$