*if*x=12(1+i3)andy=12(1i3)verify that,x3+y3=2?

1 Answer

Changing the given complex number in exponential form as follows

x=12(1+i3)=12+i32=e2π3i

y=12(1i3)=12i32=e2π3i

Hence,

x3+y3

=(e2π3i)3+(e2π3i)3

=e32π3i+e32π3i

=e2πi+e2πi

=2e2πi

=2(cos2π+isin2π)

=2(1+0)

=2

Proved