Solve the following

Question:

If |z + 2i| = |z – 2i|, then the locus of z is ____________.

Solution:

Given |z + 2i| = |z – 2i|

for z = |iy|

|x + iy + 2i| = |iy – 2i|

Squaring both sides, |x + i(+ 2)|2 = |x + i (y – 2)|2

i.e x2 + (+ 2)|2 = x2 + (– 2)|2

i.e x2 + y2 + 4 + 4y = xy2 + 4 – 4y

i.e 8= 0

i.e y = 0

∴ locus is perpendicular bisector of the segment joining (0, –2) and (0, 2)

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