InterviewSolution
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InterviewSolution
| 1. |
If `|z-i R e(z)|=|z-I m(z)|`, then prove that `z`, lies on the bisectors of the quadrants. |
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Answer» `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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