Question

Let $z\in C$ satisfy the equation $\left|z^{2}\right|+2\left(\right.z+\bar{z}\left.\right)-5=0$ , then the complex number $z+3+2i$ will lie on

• A. circle with center $1-2i$ and radius $3$
• B. circle with center $3-2i$ and radius $4$
• C. circle with center $1+2i$ and radius $3$
• D. circle with center $3+2i$ and radius $4$

Answer 1

Answer: (C)

$\left|z^{2}\right|+2\left(\right.z+\bar{z}\left.\right)-5=0:$ centre $=\left(\right.-2,0\left.\right)$ radius $=\sqrt{4 + 5}=3$
$\therefore z=-2+3e^{i \theta }\Rightarrow z+3+2i=1+2i+3e^{i \theta }$