Factorize 
.
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Answered by
1
Answer:
Whereas
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
is very simple, to factor
a
2
+
b
2
requires the use of complex numbers.
If
i
=
√
−
1
then
(
a
+
i
b
)
(
a
−
i
b
)
=
a
2
+
i
a
b
−
i
a
b
−
i
2
b
=
a
−
i
2
b
=
a
2
−
(
−
1
)
b
2
=
a
2
+
b
2
So
a
2
+
b
2
=
(
a
+
i
b
)
(
a
−
i
b
)
, but there is no other factoring with real number coefficients.
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