# Problem #1491

 1491 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 $S$? $\textbf{(A)}\ \frac12\qquad \textbf{(B)}\ \frac23\qquad \textbf{(C)}\ \frac34\qquad \textbf{(D)}\ \frac79\qquad \textbf{(E)}\ \frac78$ This problem is copyrighted by the American Mathematics Competitions.
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