Question 23
A region $S$ in the complex plane is defined by $$
\scriptsize S = \{x + iy : -1 \le x \le 1,\ -1 \le y \le 1\}.
$$
A complex number $z = x + iy$ is chosen uniformly at random from $S.$ What is the probability that $\left(\dfrac{3}{4} + \dfrac{3}{4}i\right)z$ is also in $S?$
\scriptsize S = \{x + iy : -1 \le x \le 1,\ -1 \le y \le 1\}.
$$
A complex number $z = x + iy$ is chosen uniformly at random from $S.$ What is the probability that $\left(\dfrac{3}{4} + \dfrac{3}{4}i\right)z$ is also in $S?$