Explanation

(c)
Let $z = x_{1} + iy_{1}$ and $w = x_{2} + iy_{2}$
As $|z| \leq 1$ and $|w| \leq 1$
$\Rightarrow \ \ \ \ \ x_{1}^{2} + y_{1}^{2} < 1$ and $x_{2}^{2} + y_{2}^{2} \leq 1$
Now, $|z + iw| = \left| x_{1} + iy_{1} + i\left( x_{2} + iy_{2} \right) \right| = 2$
$\Rightarrow \ \ \ \left( x_{1} - y_{2} \right)^{2} + \left( y_{1} + x_{2} \right)^{2} = 4$ ….(i)
And $\left| z - i\overline{w} \right| = \left| x_{1} + iy_{1} - i\left( x_{2} - iy_{2} \right) \right| = 2$
$\Rightarrow \ \ \left( x_{1} - y_{2} \right)^{2} + \left( y_{1} - x_{2} \right)^{2} = 4$ …(ii)
On solving Eqs. (i) and (ii), we get
$y_{1}x_{2} = 0$
$\Rightarrow \ \ \$Either $y_{1} = 0$ or $x_{2} = 0$
When $y_{1} = 0,\ \ \ \ x_{1}^{2} \leq 1$
$\Rightarrow \ \ \ \ x = \pm 1$
$\therefore\ \ \ \ z = \pm 1 + i0$