which complex number has an absolute value of 5?

$-3 + 4i$
$2 + 3i$
$7 - 2i$
$9 + 4i$

Question

which complex number has an absolute value of 5?

$-3 + 4i$
$2 + 3i$
$7 - 2i$
$9 + 4i$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Absolute Value of Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Absolute Value of Complex Numbers", "Complex Numbers" ] } ## Define the absolute value formula for a complex number $$ |a + bi| = \sqrt{a^2 + b^2} $$ ## Calculate the absolute value for each option $$ \begin{aligned} |-3 + 4i| &= \sqrt{(-3)^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \ |2 + 3i| &= \sqrt{2^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13} \ |7 - 2i| &= \sqrt{7^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53} \ |9 + 4i| &= \sqrt{9^2 + 4^2} = \sqrt{81 + 16} = \sqrt{97} \end{aligned} $$ ## Identify the correct option $$ |-3 + 4i| = 5 $$

(A) $-3 + 4i$

(B) $2 + 3i$

(C) $7 - 2i$

(D) $9 + 4i$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value of Complex Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Define the absolute value formula for a complex number

Calculate the absolute value for each option

Identify the correct option

Answer: