JEE Main 2021MathematicsComplex NumberEasyNumerical

JEE Main 2021 — Complex Number Question with Solution

JEE Main 2021 (18 Mar Shift 1)

Question

Let z1,z2 be the roots of the equation z2+az+12=0 and z1, z2 form an equilateral triangle with origin. Then, the value of a is

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Show full solutionCorrect answer: 6
Correct answer
6

Step-by-step explanation

z2+az+12=0

z1+z2=-a and z1z2=12

If 0, z1, z2 are vertices of equilateral triangles

z2=z1eiπ3

z2=z112+i32

2z2-z1=3iz1

squaring both sides

⇒4z22+z12-4z1z2=-3z12

⇒z1+z22=3z1z2

⇒a2=3×12

⇒a=6

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About this question

This is a previous-year question from JEE Main 2021, 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.