If-z-x-iy-is-a-complex-number-satisfying-z-i-2-2-z-i-2-2-then-the-locus-of-z-is-

Question Number 19739 by Tinkutara last updated on 15/Aug/17

If z = x + i y is a complex number

satisfying ∣ z + \frac{i}{2} ∣^{2} = ∣ z - \frac{i}{2} ∣^{2}, then

the locus of z is

Answered by ajfour last updated on 15/Aug/17

y = 0 (real axis)

(z + \frac{i}{2}) (\bar{z} - \frac{i}{2}) = (z - \frac{i}{2}) (\bar{z} + \frac{i}{2})

\Rightarrow z \bar{z} - \frac{iz}{2} + \frac{i \bar{z}}{2} + \frac{1}{4} = z \bar{z} + \frac{iz}{2} - \frac{i \bar{z}}{2} + \frac{1}{4}

\Rightarrow z - \bar{z} = 0

y = 0 .

Commented by Tinkutara last updated on 15/Aug/17

Thank you very much Sir!