which complex number has a distance of $\sqrt{17}$ from the origin on the complex plane?

$2 + 15i$
$17 + i$
$20 - 3i$
$4 - i$

Question

which complex number has a distance of $\sqrt{17}$ from the origin on the complex plane?

$2 + 15i$
$17 + i$
$20 - 3i$
$4 - i$

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", "Modulus of Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Absolute Value of Complex Numbers", "Modulus of Complex Numbers" ] } ## Define the modulus formula for a complex number $$ |a + bi| = \sqrt{a^2 + b^2} $$ ## Calculate the distance for each option $$ \begin{aligned} |2 + 15i| &= \sqrt{2^2 + 15^2} = \sqrt{4 + 225} = \sqrt{229} \ |17 + i| &= \sqrt{17^2 + 1^2} = \sqrt{289} = \sqrt{290} \ |20 - 3i| &= \sqrt{20^2 + (-3)^2} = \sqrt{400 + 9} = \sqrt{409} \ |4 - i| &= \sqrt{4^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \end{aligned} $$ ## Identify the correct option $$ |4 - i| = \sqrt{17} $$

(A) $2 + 15i$

(B) $17 + i$

(C) $20 - 3i$

(D) $4 - i$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define the modulus formula for a complex number

Calculate the distance for each option

Identify the correct option

Answer: