Question: Let z, w be complex numbers such that $\bar{z} + i\bar{w} = 0$ and arg$zw = \pi$, then arg z equ...

Question

Let z, w be complex numbers such that $\bar{z} + i\bar{w} = 0$ and arg $zw = \pi$ , then arg z equals

Answer 1

Sol. $\bar{z} + i\bar{w} = 0$

$\mathbf{\therefore z = iw \Rightarrow \theta + (\pi/2 + \theta) = \pi}$ , $\mathbf{\therefore}\mathbf{\theta = \pi/4}$ .

Question: Let z, w be complex numbers such that \(\bar{z} + i\bar{w} = 0\) and arg\(zw = \pi\), then arg z equ...