Assignment 14

1. Convert to rectangular coordinates. (All angles are in radians.)

a. r = 2, θ = π/3

b. r = 10, θ = 1.24

c. r = 6.3, θ = 5.8

d. r = 3, θ = 11π/4

e. r = 2, θ = -11π/6

2. Convert to polar coordinates. (Use radians.)

a. (3,5)

b. (-2,-1)

c. (0,4)

d. –2,6)

e. (1,20)

f. (.2,-.05)

3. Do the following complex arithmetic problems. Leave all answers in polar (r*e^iθ) form.

a. 2*e^iπ/4 + e^iπ/2

b. (3* e^iπ/3 ) * (4* e^-iπ/4 )

c. (1.3* e^i2.4)/(2.1* e^i1.3)

d. (2+3i)/(1+7i)

4. Find all solutions; put in both rectangular and polar form.

a. z² = 1 + 2i

b. z³ = -1

c. z⁴ = i

d. z² + 2iz – 1 = 0