JEE Main 2014MathematicsComplex NumberMediumMCQ

JEE Main 2014 — Complex Number Question with Solution

JEE Main 2014 (19 Apr Online)

Question

For all complex numbers z of the form 1+iα, α∈R, if z2=x+iy, then 

Choose an option

Show full solutionCorrect option: B
Correct answer
By2+4x-4=0

Step-by-step explanation

Given z=1+iα, z2=x+iy

⇒1+iα2=x+iy

⇒12+i2α2+2iα=x+iy

Using i2=-1,

⇒1-α2+2iα=x+iy

Equating the real and imaginary parts, we get

x=1-α2 and y=2α

⇒α2=1-x and y2=4α2

⇒y2=41-x

⇒y2=4-4x

⇒y2+4x-4=0.

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About this question

This is a previous-year question from JEE Main 2014, 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.