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Mathematics
Mathematics
Problem
If
(
x
+
i
y
)
1
/
3
=
a
+
i
b
(x+i y)^{1 / 3}=a+i b
(
x
+
i
y
)
1/3
=
a
+
ib
, where
x
,
y
,
a
,
b
∈
R
x, y, a, b \in \mathbb{R}
x
,
y
,
a
,
b
∈
R
, then show that
x
a
−
y
b
=
−
2
(
a
2
+
b
2
)
\frac{x}{a}-\frac{y}{b}=-2\left(a^{2}+b^{2}\right)
a
x
−
b
y
=
−
2
(
a
2
+
b
2
)
.
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