ACT Math Practice Question #1619 (Hard (640)) | Test Citadel
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ACT Math Difficulty: Hard (640)

Digital ACT Math Practice Question #1619

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What is the complex quotient \(\frac{4 + 2i}{1 - i}\), where \(i = \sqrt{-1}\)?
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Multiply by (1+i)/(1+i). Denominator is always 1^2 + 1^2 = 2. Numerator: (4-2) + (4+2)i = 2 + 6i. Divide by 2 -> 1 + 3i.

Masterclass Solution & Distractor Trap Analysis

Multiply numerator and denominator by the complex conjugate \(1 + i\): \(\frac{(4 + 2i)(1 + i)}{(1 - i)(1 + i)} = \frac{4 + 4i + 2i + 2i^2}{1 - i^2}\). Since \(i^2 = -1\), numerator = \(4 + 6i - 2 = 2 + 6i\), denominator = \(1 - (-1) = 2\)....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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