JEE Main 2024MathematicsComplex NumberMediumMCQ

JEE Main 2024 — Complex Number Question with Solution

JEE Main 2024 (01 Feb Shift 2)

Question

If z is a complex number such that z≤1, then the minimum value of z+123+4i is:

Choose an option

Show full solutionCorrect option: C
Correct answer
C32

Step-by-step explanation

Given: z+3+4i2; z≤1

Let, z=x+iy

And z=1 gives x2+y2=1, which represents a circle having centre at 0,0 and radius as 1 unit.

Now, z+3+4i2 gives the distance of z from -32,-2

So, we need to find the minimum distance of AP.

⇒AP=OP-OA

⇒AP=-32-02+0+22-1

⇒AP=94+4-1

⇒AP=52-1

⇒AP=32

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About this question

This is a previous-year question from JEE Main 2024, 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.