1.) Find all solutions of the equation. Leave answers in trigonometric form.

Question

x^2 + 1 - sqrt3i = 0

2.) Give the rectangular coordinates for the point.
(9, 2pi/3)

3.) The rectangular coordinates of a point are given. Express the point in polar coordinates with r L 0 and 0° K theta < 360°.

(1/4 , -sqrt3/4)

4.) For the given rectangular equation, give its equivalent polar equation.
8x - 7y = -10

I need help setting this up.

Answer 1

#1
in polar form,
-1+√3i = (2,2π/3)
So, the two square roots of that are
(√2,π/3) and (√2,4π/3)

#2,#3
just plug in
x = r cosθ
y = r sinθ

#4
8x - 7y = -10
7y - 8x = 10
7r sinθ - 8r cosθ = 10
r = 10/(7sinθ-8cosθ)