if the complex number (x = 3 + bi) and (|x|^2 = 13), which is a possible value of (b)?

2
4
9
10

Question

if the complex number (x = 3 + bi) and (|x|^2 = 13), which is a possible value of (b)?

2
4
9
10

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Numbers", "Solving Quadratic Equations" ], "new_concepts": [ "Absolute Value of Complex Numbers", "Modulus of Complex Numbers" ], "current_concepts": [ "Complex Numbers", "Solving Quadratic Equations", "Absolute Value of Complex Numbers", "Modulus of Complex Numbers" ] } ## Express the squared modulus of the complex number $$ \begin{aligned} &x = 3 + bi \ &|x|^2 = 3^2 + b^2 = 9 + b^2 \end{aligned} $$ ## Set up the equation and solve for b $$ \begin{aligned} &9 + b^2 = 13 \ &b^2 = 4 \ &b = \pm 2 \end{aligned} $$ ## Identify the matching option $$ b = 2 $$

(A) 2

(B) 4

(C) 9

(D) 10

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Express the squared modulus of the complex number

Set up the equation and solve for b

Identify the matching option

Answer: