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
$=\sqrt{2^{2}+3^{2}-4}=3$