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Mathematics
Mathematics
Problem
If
a
+
i
b
=
(
x
+
i
)
2
2
x
2
+
1
a + ib = \frac{(x+i)^2}{2x^2+1}
a
+
ib
=
2
x
2
+
1
(
x
+
i
)
2
, prove that
a
2
+
b
2
=
(
x
2
+
1
)
2
(
2
x
2
+
1
)
2
a^2 + b^2 = \frac{(x^2+1)^2}{(2x^2+1)^2}
a
2
+
b
2
=
(
2
x
2
+
1
)
2
(
x
2
+
1
)
2
.
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