Question:
If z = x + iy, then show that zz̅ + 2(z + z̅) + b = 0 where bϵR, representing z in the complex plane is a circle.
Solution:
According to the question,
We have,
z = x + iy
⇒ z̅ = x – iy
Now, we also have,
z z̅ + 2 (z + z̅) + b = 0
⇒ (x + iy) (x – iy) + 2 (x + iy + x – iy) + b = 0
⇒ x2 + y2 + 4x + b = 0
The equation obtained represents the equation of a circle.
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