Please write clearly Instructions. Twenty-five points. We will use the accompany
ID: 3103072 • Letter: P
Question
Please write clearly
Instructions. Twenty-five points. We will use the accompanying rubric. We know that the set C* of all non-zero complex number is an Abelian group. Recall that for z = a + bi C, we can write z = r(cos theta + i sin theta), where r = a2 + b2 and tan theta = b/a if a 0 and theta = plusminus pi/2 if a = 0. Example: 1 + i = 2(cos pi/4 + i sin pi/4), i = cos pi/2 + i sin pi/2, -1 = cos pi + i sin pi. We have the following identities: cos theta + i.sin theta= 1 if and only if theta = 2pik for some integer k; and For z = r(cos theta + i sin theta). zn = rn(cos(n theta) + i sin(n theta)). DeMoivre's Theorem For z = r(cos theta + i sin theta) C* of finite order, that is zn = 1 for some n > 0, what must r be? What must theta be?Explanation / Answer
i dont no