ACT Math Practice Question #1320 (Medium (31)) | Test Citadel
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ACT Math Difficulty: Medium (31)

Digital ACT Math Practice Question #1320

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

If $z = 9 - 40i$ where $i = \sqrt-1$, what is the absolute value (modulus) of $z$, denoted $|z|$?
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Socratic AI Engine Step-by-Step Derivation
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Recognize standard Pythagorean triples: $9-40-41$. The modulus is instantly $41$.

Masterclass Solution & Distractor Trap Analysis

The modulus of a complex number $z = a + bi$ is defined as $|z| = \sqrt{a^2 + b^2}$. $$|z| = \sqrt{9^2 + (-40)^2} = \sqrt{81 + 1600} = \sqrt{1681} = 41.$$...

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

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