Express the following complex numbers in standard form $$\left(\frac{\sqrt 3}{2}+\frac{i}{2}\right)^{25}$$
I know that you have to put it in the form $\cos\theta+i\sin \theta$ but I'm not sure how to go about it. 

When you want to raise a number to an integer power, the polar form is very handy. When in doubt, draw a picture-plot $\frac {\sqrt 3}2+\frac i2$. You should notice that the radius is about $1$.  Do you know how to compute the radius and find it is exactly $1$?  Then you should know that $(re^{i\theta})^n=r^ne^{in\theta}$  You should recognize the angle.
