JEE Main 2020MathematicsComplex NumberHardMCQ

JEE Main 2020 — Complex Number Question with Solution

JEE Main 2020 (02 Sep Shift 1)

Question

The value of 1+sin2π9+icos2π91+sin2π9−icos2π93 is 

Choose an option

Show full solutionCorrect option: C
Correct answer
C-12(3-i)

Step-by-step explanation

1+sin2π9+icos2π91+sin2π9−icos2π93

=1+cos5π18+isin5π181+cos5π18-isin5π183=2cos25π36+i2sin5π36·cos5π362cos25π36-i2sin5π36·cos5π363

=cos5π36+isin5π36cos5π36-isin5π363=cos5π36+isin5π366

=cos6×5π36+isin6×5π36=cos5π6+isin5π6

=-32+i12

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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.