Use DeMoivre's Theorem to write the complex number in trigonometric form.
(cos pi/4 + I sinpi/4)^3

Question

Use DeMoivre's Theorem to write the complex number in trigonometric form. 
(cos pi/4 + I sinpi/4)^3

zepdrix · Answer

Ooo these are so fun :)

anonymous · Answer

I hope that means that you are good at them

zepdrix · Answer

Hmm it's already in trig form...
I guess we just apply DeMoivre's Theorem directly from here.$$\Large\rm \left(\cos \frac{\pi}{4}+\mathcal i \sin \frac{\pi}{4}\right)^3$$Applying DeMoivre, just bring the 3 inside,$$\Large\rm \left(\cos \frac{3\pi}{4}+\mathcal i \sin \frac{3\pi}{4}\right)$$Yah?

anonymous · Answer

well you just made it look easy thanks

zepdrix · Answer

They get a little trickier when they give them to you in a+bi form and make you convert to trig before you can apply DeMoivre...
But yah they start out nice and easy! :)

anonymous · Answer

$$\left( \cos \theta +\iota \sin \theta  \right)^n=\cos n \theta+\iota \sin  n \theta$$