SAT Math Practice Question #24068 - SATify | SATify

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SAT Math Practice Question #24068 - SATify | SATify

#24068

complex numbers

probability

hard

150 sec

A region $S$ in the complex plane is defined by $S = x + i y : - 1 \leq x \leq 1, - 1 \leq y \leq 1$ . A complex number $z = x + i y$ is chosen uniformly at random from $S$ . What is the probability that $(2 + 2 i) z$ is also in $S$ ?

A.

$\frac{1}{2}$

B.

$\frac{1}{4}$

C.

$\frac{1}{6}$

D.

$\frac{1}{8}$

E.

$\frac{1}{16}$