Complex Numbers: If z is a complex number such that |z|le1 , then the minimum value… | JEE Main 2024 | Yukti Vault

Yukti Vault

JEE Main 2024 (Online) 1st February Evening ShiftQuestion 1

If $z$ is a complex number such that $|z|\le1$, then the minimum value of $\left|z+\frac12(3+4i)\right|$ is :

Complex Numbers

$2$$\frac52$$\frac32$✓ Correct answer$3$

Solution

$|z-(-\frac32-2i)|$ is the distance from $z$ to a point at distance $\frac52$ from the origin; over $|z|\le1$ the minimum is $\frac52-1=\frac32$.

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