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If z=x+i y , then show that z z +2(z+ ...

If `z=x+i y ,` then show that `z z +2(z+ z )+a=0` , where `a in R ,` represents 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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