00:01
So for this problem, we want to write parametric equations, and we know that we are given a complex number with an a value of negative 1, a b of positive 1, and we want to use n to be t.
00:14
And so to find our number raised, or a complex number raised to the n power, we know that we're going to use demov's theorem.
00:22
And so first we can go ahead and calculate our r and theta.
00:25
So we know r is equal to the square root of a squared plus b squared, which in our case is going to be equal to the square root of 2.
00:33
And theta is equal to the inverse tangent of b over a, which here is going to be 3 pi over 4.
00:42
And so now we can go ahead and plug these into our equation.
00:46
So we find that our complex number raised to the n power, which we're going to again substitute in t for n, is going to be r to the.
00:57
The n power, which is the square of 2 to the t power, times the cosine of n theta, which becomes a t times 3 pi over 4...