# Math Help - Complex Numbers problem

1. ## Complex Numbers problem

Calculate: (1+3i)^9

How do I solve this? I have tried without any success. Thanks!

2. Originally Posted by sf1903
Calculate: (1+3i)^9
$1 + i\sqrt 3 = 2\cos \left( {\frac{\pi }
{3}} \right) + i2\sin \left( {\frac{\pi }
{3}} \right)$

$2^9=512$ and $9\left(\frac{\pi}{3}\right)=3\pi$

3. Hint : $2e^{i\pi/3}=1+\sqrt{3}i$.

4. Originally Posted by Plato
$1 + i\sqrt 3 = 2\cos \left( {\frac{\pi }
{3}} \right) + i2\sin \left( {\frac{\pi }
{3}} \right)$

$2^9=512$ and $9\left(\frac{\pi}{3}\right)=3\pi$
If im correct the answer should be -512

512*Cos(3π)+i*512*Sin(3π) = -512 + 0 = -512

Or am i out in the blue?

5. Yes! $(2e^{i\pi/3})^9=512e^{3i\pi}=-512$.