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Mathematics
Problem
Let
z
z
z
be a non-real complex number lying on
∣
z
∣
=
1
|z| = 1
∣
z
∣
=
1
. Prove that
z
=
1
+
i
tan
(
arg
(
z
)
2
)
1
−
i
tan
(
arg
(
z
)
2
)
(
where
i
=
−
1
)
.
z = \frac{1+i \tan\left(\frac{\arg(z)}{2}\right)}{1-i \tan\left(\frac{\arg(z)}{2}\right)} \quad (\text{where } i = \sqrt{-1}).
z
=
1
−
i
tan
(
2
a
r
g
(
z
)
)
1
+
i
tan
(
2
a
r
g
(
z
)
)
(
where
i
=
−
1
)
.
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