Question

By writing the complex number in the form z = Re^(iθ),find a

Answer 1

Firstly,we can write the complex number in the form z = Re^(iθ).And,it is,

1+i=(2^0.5)e^(iπ/4)

so,we can obtain,

(1+i)^20

=(2^10)e^(5πi)

=1024×e^(5πi)

=1024×e^(πi)

=1024×(cosπ+isinπ)

=-1024

Come on! I hope you can get it.It is so easy!