Explanation

(d)
Let $z = r_{1}e^{i\theta}\ \ \ \ \Rightarrow \ \ \ \ \ \ \overline{z} = r_{1}e^{- i\theta}$ and $w = r_{2}e^{i\varnothing}$
Given, $|zw| = 1$
$\Rightarrow \ \ \ \ \ |r_{1}e^{i\theta}.r_{2}e^{i\varnothing}| = 1\ \ \ \ \ \Rightarrow \ \ \ r_{1}r_{2} = 1$ …(i)
And $\arg{(z) - \arg{(w) = \frac{\pi}{2}\ \ \ \ \ \ \ \Rightarrow \ \ \ \ \theta - \varnothing = \frac{\pi}{2}}}$ …(ii)
Now, $\overline{z}w = r_{1}e^{- i\theta}.r_{2}e^{i\varnothing} = r_{1}r_{2}r^{- i(\theta - \varnothing)}$
$= 1.e^{- i\pi/2} = \cos{\frac{\pi}{2} - i\sin\frac{\pi}{2}}$
[from Eqs. (i) and (ii)]
$\Rightarrow \ \ \ \ \overline{z}w = - i$