Recall that complex number have the form a + bi, where a and b are real. These

Question:

Recall that complex number have the form a + bi, where a and b are real. These numbers behave much like the real numbers, with the proviso and i2 = -1. Show each of the following:
(a) ebi = cos b + i and b: Use the Macluarin series for ea, cos u, and sin u.
(b) ea+bi = ea(cos b + i sin b)
(c) Dx e(a+βi)x = (a + βi)e (a+βi)x