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Mathematics
Mathematics
Problem
If
∣
z
−
i
Re
(
z
)
∣
=
∣
z
−
Im
(
z
)
∣
|z - i \operatorname{Re}(z)| = |z - \operatorname{Im}(z)|
∣
z
−
i
Re
(
z
)
∣
=
∣
z
−
Im
(
z
)
∣
, then prove that
z
z
z
lies on the bisectors of the quadrants, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
.
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