Question

The equation $z\overline{z}+(2-3i)z+(2+3i)\overline{z}+4=0$ represents a circle of radius

• A. $2$
• B. $3$
• C. $4$
• D. $6$

Answer 1

Answer: (B)

Let $z=z+iy$, therefore given equation becomes
$(x+iy)(x-iy)+(2-3i)(x+iy)$
$+(2+3i)(x-iy)+4=0$
$\Rightarrow x^2+y^2+2x+3y-2iy$
$+2x-2iy+3ix+3y+4=0$
$\Rightarrow x^2+y^2+4x+6y+4=0$
which represents a circle with radius
$=\sqrt{2^2+3^2-4}=3$