JEE Main 2023MathematicsComplex NumberMediumMCQ

JEE Main 2023 — Complex Number Question with Solution

JEE Main 2023 (10 Apr Shift 2)

Question

Let S=z=x+iy:2z-3i4z+2i is a real number }. Then which of the following is NOT correct?

Choose an option

Show full solutionCorrect option: B
Correct answer
B (x,y)=0,-12
 

Step-by-step explanation

We have,

Z=2z-3i4z+2i

⇒Z=2x+i2y-34x+i4y+2

⇒Z=2x+i2y-34x+i4y+2×4x-i4y+24x-i4y+2

⇒Z=8x2+4y+22y-3+i4x2y-3-8xy+4x16x2+4y+22

Since, Z is purely real, so 4x2y-3-8xy+4x16x2+4y+22=0

⇒-12x+8xy-8xy+4x=0

⇒x=0

And,

4x+i4y+2≠0

⇒i4y+2≠0

⇒y≠-12

Hence this is the required option.

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Complex Number chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2023, 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.