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The equation

Question:

The equation $|\mathrm{z}-\mathrm{i}|=|\mathrm{z}-1|, \mathrm{i}=\sqrt{-1}$, represents:

1. the line through the origin with slope $-1$.

2. a circle of radius 1 .

3. a circle of radius $\frac{1}{2}$.

4. the line through the origin with slope $1 .$

Correct Option: , 4

Solution:

$|z-i|=|z-1|$

$y=x$