[SOLVED] Amath 567, problem set 1

1. Problem 1: Express each of the following in polar exponential form.
(a) −i
(b) 1 + i
(c) 1
2 +
√
3
2
i2. Problem 2: Express each of the following in the form of a + bi, where a
and b are real.
(a) e
2+iπ/2
(b) 1
1+i
(c) (1 + i)
3
(d) |3 + 4i|
(e) cos(iπ/4 + c), where c is real.3. Problem 3: Solve for the roots of the following equations.
(a) z
3 = 4
(b) z
4 = −14. Problem 4: Establish the following results.
(a) (z + w)∗ = z ∗ +w∗
(b) ℜ(z) ≤ |z|
(c) |wz ∗ +w ∗ z| ≤ 2|wz|
(d) |z1z2| = |z1||z2|