If $z = 2 + 3i$, then $z^5 + (\overline{z})^5$ is equal to :

JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 29 July 2022, Shift 1, Maths Q2

Question 2 of 90 in this shift, Maths question 2 of 30, Section A.

z = 2 + 3i

, then

z^5 + (\overline{z})^5

is equal to :

(1)244Official answer
(2)224
(3)245
(4)265

Official answer

Option 1

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Complex Numbers - Polar Form
Idea tested: Simplifying Conjugate Binomial Sums

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.