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Mathematics
Problem
If
1
−
i
x
1
+
i
x
=
a
−
i
b
\frac{1-ix}{1+ix} = a - ib
1
+
i
x
1
−
i
x
=
a
−
ib
and
a
2
+
b
2
=
1
a^2 + b^2 = 1
a
2
+
b
2
=
1
, where
a
,
b
∈
R
a, b \in \mathbb{R}
a
,
b
∈
R
and
i
=
−
1
i = \sqrt{-1}
i
=
−
1
, then
x
x
x
is equal to a.
2
a
(
1
+
a
)
2
+
b
2
\frac{2a}{(1+a)^2 + b^2}
(
1
+
a
)
2
+
b
2
2
a
b.
2
b
(
1
+
a
)
2
+
b
2
\frac{2b}{(1+a)^2 + b^2}
(
1
+
a
)
2
+
b
2
2
b
c.
2
a
(
1
+
b
)
2
+
a
2
\frac{2a}{(1+b)^2 + a^2}
(
1
+
b
)
2
+
a
2
2
a
d.
2
b
(
1
+
b
)
2
+
a
2
\frac{2b}{(1+b)^2 + a^2}
(
1
+
b
)
2
+
a
2
2
b
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