Q8 of 66 Page 91

If z = x + iy, then show that where bϵR, representing z in the complex plane is a circle.

Given z = x + iy


⇒ z̅ = x – iy


Now, z z̅ + 2 (z + z̅) + b = 0


⇒ (x + iy) (x – iy) + 2 (x + iy + x – iy) + b = 0


⇒ x2 + y2 + 4x + b = 0


This is the equation of a circle.


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