ACT Math Practice Question #1201 (Hard (34)) | Test Citadel
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ACT Math Difficulty: Hard (34)

Digital ACT Math Practice Question #1201

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

If $i = \sqrt{-1}$, what is the value of the complex expression $\frac{5 - 3i}{2 + 4i}$ in standard form $a + bi$?
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Immediately calculate the denominator: $2^2 + 4^2 = 20$. For the real numerator: $5(2) + (-3)(-4)(-1) = 10 - 12 = -2$. The real part must be $-2/20 = -1/10$, which instantly isolates Choice B without finishing the imaginary part.

Masterclass Solution & Distractor Trap Analysis

Multiply numerator and denominator by the complex conjugate of the denominator, $(2 - 4i)$: $$\frac{(5 - 3i)(2 - 4i)}{(2 + 4i)(2 - 4i)} = \frac{10 - 20i - 6i + 12i^2}{2^2 - (4i)^2} = \frac{10 - 26i + 12(-1)}{4 - 16(-1)} = \frac{10 - 26i - 1...

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

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