JEE Main 2020MathematicsComplex NumberMediumMCQ

JEE Main 2020 — Complex Number Question with Solution

JEE Main 2020 (04 Sep Shift 2)

Question

If a and b are real numbers such that 2+α4=a+bα, where α=-1+i32, then a+b is equal to:

Choose an option

Show full solutionCorrect option: A
Correct answer
A9

Step-by-step explanation

 2+α4=a+bα
4+α2+4α2=a+bα

Now using, α=-1+i32⇒2α+12=i32

⇒α2=-1+α

So, a+bα=4-α-1+4α2

a+bα=3+3α2=91+2α+α2
a+bα=91+2α+-1-α=9α

⇒a=0, b=9⇒a+b=9

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About this question

This is a previous-year question from JEE Main 2020, 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.