The values of zfor which |z + i|, = ,|z - i| | vedclass

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Question

(a) Let $z = x + iy$......$(i)$
Given $|z + i|\, = \,|z - i|$
or $|x + iy + i|\, = \,|x + iy - i|$
or $|x + i(y + 1)|\, = \,|x + i(y - 1)|$
or $\s

Vedclass · Accepted Answer

Any real number

Vedclass · Answer

(a) Let $z = x + iy$......$(i)$
Given $|z + i|\, = \,|z - i|$
or $|x + iy + i|\, = \,|x + iy - i|$
or $|x + i(y + 1)|\, = \,|x + i(y - 1)|$
or $\sqrt {{x^2} + \,{{(y + 1)}^2}} = \sqrt {{x^2} + {{(y - 1)}^2}} $
or ${x^2} + {(y + 1)^2} = {x^2} + {(y - 1)^2}$
or ${y^2} + 2y + 1 = {y^2} - 2y + 1$or $4y = 0$or $y = 0$
Hence from $(i)$, we get $z = x$, where $x$ is any real number.

The values of $z$for which $|z + i|\, = \,|z - i|$ are

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