MyGoalPrep LogoMyGoalPrep.com

General — Hard JEE math MCQ

Let $S$ be the set of all complex numbers $Z$ satisfying $|z-2+i| \geq \sqrt{5}$. If the complex number $Z_{0}$ is such that $\frac{1}{\left|Z_{0}-1\right|}$ is the maximum of the set $\left\{\frac{1}{|z-1|}: z \in S\right\}$, then the principal argument of $\frac{4-z_{0}-\overline{z_{0}}}{Z_{0}-\overline{z_{0}}+2 i}$ is
  1. A. $-\frac{\pi}{2}$
  2. B. $\frac{\pi}{4}$
  3. C. $\frac{\pi}{2}$
  4. D. $\frac{3 \pi}{4}$

Solution

The correct option is **A**.

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
Let SS be the set of all complex numbers ZZ satisfying ∣z−2+i∣≥5|z-2+i| \geq \sqrt{5}. If the complex number Z0Z_{0} is such that 1∣Z0−1∣\frac{1}{\left|Z_{0}-1\right|} is the maximum of the set {1∣z−1∣:z∈S}\left\{\frac{1}{|z-1|}: z \in S\right\}, then the principal argument of 4−z0−z0‾Z0−z0‾+2i\frac{4-z_{0}-\overline{z_{0}}}{Z_{0}-\overline{z_{0}}+2 i} is
AI hints
Ask for a nudge. Keep it specific.