The values of z for which |z + i| = |z - i| a | vedclass

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(A) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Given $|z + i| = |z - i|$.Substituting $z = x + iy$:$|x + iy + i| = |x + iy - i|$$|x + i(y + 1)| = |x

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Any real number

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(A) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Given $|z + i| = |z - i|$.Substituting $z = x + iy$:$|x + iy + i| = |x + iy - i|$$|x + i(y + 1)| = |x + i(y - 1)|$Squaring both sides:$x^2 + (y + 1)^2 = x^2 + (y - 1)^2$$x^2 + y^2 + 2y + 1 = x^2 + y^2 - 2y + 1$$2y = -2y$$4y = 0 \implies y = 0$.Since $y = 0$,$z = x + i(0) = x$,which represents any real number.

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

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