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Sample Question 23:
A region \(S\) in the complex plane is defined by \(S = \{x + iy: - 1\le x\le1, - 1\le y\le1\}.\) A complex number \(z = x + iy\) is chosen uniformly at random from \(S\). What is the probability that \(\left(\frac34 + \frac34i\right)z\) is also in \(S\)?
\(\textbf{(A)}\ \frac12\qquad \textbf{(B)}\ \frac23\qquad \textbf{(C)}\ \frac34\qquad \textbf{(D)}\ \frac79\qquad \textbf{(E)}\ \frac78\)