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Mathematics
Problem
6. If
a
+
i
b
=
(
x
+
i
)
2
2
x
2
+
1
a+i b=\frac{(x+i)^{2}}{2 x^{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{\left(x^{2}+1\right)^{2}}{\left(2 x^{2}+1\right)^{2}}
a
2
+
b
2
=
(
2
x
2
+
1
)
2
(
x
2
+
1
)
2
.
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