SAT Math Practice Question #25970 - SATify | SATify

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SAT Math Practice Question #25970 - SATify | SATify

#25970

complex numbers

algebra

hard

120 sec

Let $z = \frac{3 + i}{2}$ . What is $(\sum_{k = 1}^{24} z^{k^{2}}) (\sum_{k = 1}^{24} \frac{1}{z ^{k^{2}}})$ ?

A.

$48$

B.

$72$

C.

$96$

D.

$108$

E.

$144$