Calculating exponent of complex number.

[charmedbeauty]

Homework Statement

z= 1+i√3
find z^9

Homework Equations

The Attempt at a Solution

Arg(z) = pi/3 and |z|=2


so z= 2e^i*pi/3

so z^9 = 2^9 (cos6pi +isin 6pi)

= 512(1) =512
but the answer has negative 512?

 

[SammyS]

Homework Statement

z= 1+i√3
find z^9

Homework Equations

The Attempt at a Solution

Arg(z) = pi/3 and |z|=2

so z= 2e^i*pi/3

so z^9 = 2^9 (cos6pi +isin 6pi)

= 512(1) =512
but the answer has negative 512?

What is \displaystyle \left(2\,e^{i\pi/3}\right)^9\,?

 

[charmedbeauty]

What is \displaystyle \left(2\,e^{i\pi/3}\right)^9\,?

512*(cos 3pi +isin3pi)

= 512(-1) =-512

THANKS!