Find-center-and-radius-of-circle-having-equation-zz-1-i-z-1-i-z-1-0-

Question Number 19555 by Tinkutara last updated on 12/Aug/17

Find center and radius of circle having

equation z \bar{z} + (1 - i) z + (1 + i) \bar{z} - 1 = 0 .

Answered by ajfour last updated on 12/Aug/17

Equation of circle :

∣ z - z_{0} ∣= r

\Rightarrow (z - z_{0}) (\bar{z} - {\bar{z}}_{0}) = r^{2}

or z \bar{z} - {\bar{z}}_{0} z - z_{0} \bar{z} + ∣ z_{0} ∣^{2} - r^{2} = 0

comoparing this with given eqn .

z_{0} = 1 + i and r = \sqrt{1 + ∣ z_{0} ∣^{2}} = \sqrt{3} .

Commented by Tinkutara last updated on 12/Aug/17

Thank you very much Sir!