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Question
If z = x + iy, then show that `z barz + 2(z + barz) + b` = 0, where b ∈ R, represents a circle.
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Solution
Given that: z = x + iy
To prove: `z barz + 2(z + barz) + b` = 0
⇒ (x + iy) (x – iy) + 2(x + iy + x – iy) + b = 0
⇒ x2 + y2 – 2(x + x) + b = 0
⇒ x2 + y2 – 4x + b = 0
Which represents a circle.
Hence proved.
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