if X + iY =3√A+IB then show thatX-iY=3√a-ib
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Answer:
x+iy)=(a+ib)
3
a
3
+(ib)
3
+3abi(a+ib)
x+iy=a
3
−ib
3
+3a
2
bi−3ab
2
∴x=a
3
−3ab
2
,y=−b
3
+3a
2
b
⇒
a
x
=a
2
−3b
2
,
b
y
=−b
2
+3a
2
so,
a
x
+
b
y
=4a
2
−4b
2
=4(a
2
−b
2
)
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