how do you do this?

[nilkn]

<p>

@MNOAAA12

i believe its true for all values of n because the magnetude of the equation is 1 (the coefficient in front of the cos/sin is 1) i think. Ive never seen it written like that tho.

</p>

<p>True, the absolute value of z raised to any power will be 1. However, by Euler’s formula, there exists an angle theta such that z = exp(i*theta). Now examine what happens:</p>

<p>z^n = [exp(i<em>theta)]^n = exp(i</em>n*theta)</p>

<p>The result is a new complex number of the same magnitude but a different angle. So in other words complex numbers not only can increase in magnitude when raised to a power–they also can rotate about the origin.</p>

<p>[By the way, in this case theta is trivially 30 degrees.]</p>