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If z= x+iy, "then show that " z barz + 2...

If `z= x+iy, "then show that " z barz + 2(z + barz) +b = 0, where b ∈R,"respresents a circle"`.

Text Solution

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Given that z = x + iy
Then, barz = x- iy
Now, `zbarz +2(z+barz) + b = 0`
`rArr (x +iy)(x-iy)+2(x+iy+x-iy)+ b = 0 `
`rArr x^(2) + y^(2) _3x + b = 0, `which is tha equation of a circle.
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