ACT Math Practice Question #1319 (Medium (31)) | Test Citadel
TC
Test Citadel
ACT Math Difficulty: Medium (31)

Digital ACT Math Practice Question #1319

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

If $z = 7 + 24i$ where $i = \sqrt-1$, what is the absolute value (modulus) of $z$, denoted $|z|$?
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
⚡ 15-Second Desmos Speed Hack

Recognize standard Pythagorean triples: $7-24-25$. The modulus is instantly $25$.

Masterclass Solution & Distractor Trap Analysis

The modulus of a complex number $z = a + bi$ is defined as $|z| = \sqrt{a^2 + b^2}$. $$|z| = \sqrt{7^2 + (24)^2} = \sqrt{49 + 576} = \sqrt{625} = 25.$$...

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

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.