what is the distance from the origin to point a graphed on the complex plane below?

$\sqrt{5}$
$\sqrt{13}$
9
13

Question

what is the distance from the origin to point a graphed on the complex plane below?

$\sqrt{5}$
$\sqrt{13}$
9
13

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Complex Plane Representation", "Absolute Value of Complex Numbers", "Modulus of Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Complex Plane Representation", "Absolute Value of Complex Numbers", "Modulus of Complex Numbers" ] } ## Identify coordinates of point A $$ A = (-3, -2) \implies z = -3 - 2i $$ ## Apply distance formula from origin $$ d = \sqrt{(-3)^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} $$

(A) $\sqrt{5}$

(B) $\sqrt{13}$

(C) 9

(D) 13

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

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QUESTION IMAGE

Question

Explanation:

Identify coordinates of point A

Apply distance formula from origin

Answer: