JEE Main 2021MathematicsComplex NumberMediumMCQ

JEE Main 2021 — Complex Number Question with Solution

JEE Main 2021 (26 Aug Shift 2)

Question

If (3+i)100=299(p+iq), then p and q are roots of the equation :

Choose an option

Show full solutionCorrect option: D
Correct answer
Dx2-(3-1)x-3=0

Step-by-step explanation

(3+i)100=299(p+iq)

2100cosπ6+isinπ6100=299p+iq

2100ei50π3=299p+iq

2cos50π3+isin50π3=p+iq

2cos17π-π3+isin17π-π3=p+iq

2-cosπ3+isinπ3=p+iq

2-12+i32=p+iq

p=-1 & q=3

p and q Roots of the equation
x2-(3-1)x-3=0

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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.