JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q2 · Dronacharya Exams

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MathematicsSingle correct+4 / -1Question 2 of 90

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

A

244

B

224

C

245

D

265

Answer and worked solution

Official answer: A

Powers. $z^2=-5+12i$ , $z^4=-119-120i$ , $z^5=122-597i$ .

Sum $z^5+\bar z^5=2\operatorname{Re}z^5=244$ .

(A)

Topics:Algebra of complex numbers Binomial expansion

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