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If |z-i R e(z)|=|z-I m(z)| , then prove ...

If `|z-i R e(z)|=|z-I m(z)|` , then prove that `z` , lies on the bisectors of the quadrants.

Text Solution

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`z = x +iy`
`rArr Re (z) = x, Im (z) = y`
`|z - iRe(z)|=|z- Im (z)|`
`rArr |x + iy -ix|=|x + iy -y|`
`rArr x^(2) +(x-y)^(2) = (x-y)^(2) + y^(2)`
`rArr x^(2) = y^(2)`
` rArr |x| = |y|`
Hence, z lies on the bisectors the quadrants.
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