JEE Main 2015MathematicsComplex NumberMediumMCQ

JEE Main 2015 — Complex Number Question with Solution

JEE Main 2015 (11 Apr Online)

Question

If z is a non-real complex number, then the minimum value of Im z5Im z5 is (Where Im z = Imaginary part of z)

Choose an option

Show full solutionCorrect option: B
Correct answer
B-4

Step-by-step explanation

Let, z=r(cosθ+isinθ)

z 5 = r 5 (cos5θ+isin5θ)

Imz5=r5sin5θ

and Im z5=r5sin5θ

Im (z5)Im z5= sin5θsin5θ=A (Let)

⇒dAdθ=5sin5θcos5θ-5sin5θsin4θcosθsin5θ2

⇒dAdθ=5sin4θsinθcos5θ-sin5θcosθsin10θ

⇒ dA dθ = 5 sin 6 θ sin −4θ =0

⇒θ=π4

The minimum value of A will be at  θ=π4.

⇒A=sin5π4sinπ45
=-12125

=-24=-4

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About this question

This is a previous-year question from JEE Main 2015, covering the Complex Number chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.