JEE Main 2019MathematicsComplex NumberMediumMCQ

JEE Main 2019 — Complex Number Question with Solution

JEE Main 2019 (09 Jan Shift 2)

Question

Let z0 be a root of quadratic equation, x2+x+1=0.  If z=3+6iz081-3iz093 , then arg z is equal to:

Choose an option

Show full solutionCorrect option: B
Correct answer
Bπ4

Step-by-step explanation

z0=w or w2

When z0=w

z=3+6i×w81-3i×w93

=3+6i-3i=3+3i

When z0=w2

z=3+6i×w281-3i×w293

=3+6i-3i=3+3i

∴arg⁡z=tan-1ImzRez=tan-1⁡33=π4

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About this question

This is a previous-year question from JEE Main 2019, 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.