Compute (5 - 3i)³.

A125 + 27i

B125 - 27i

C-10 - 198i

D-10 + 198i

Answer & Solution

Correct answer: C. -10 - 198i

(a - b)³ = a³ - 3a²b + 3ab² - b³. Here a = 5, b = 3i. a³ = 125. 3a²b = 3·25·3i = 225i. 3ab² = 3·5·(3i)² = 15·(-9) = -135. b³ = (3i)³ = 27i³ = -27i. **Sum:** 125 - 225i + (-135) - (-27i) = (125 - 135) + (-225 + 27)i = -10 - 198i.

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