Question

1.) Write the complex number in trigonometric form r(cos theta + i sin theta) with theta in the interval [0°, 360°).

9 sqrt 3 + 9i

2.) Find the product. Write the product in rectangular form, using exact values.
[4 cis 30°] [5 cis 120°]

3.) [4(cos 135° + i sin 135°)][6(cos 225° + i sin 225°)]

4.) Find the following quotient, and write the quotient in rectangular form, using exact values.
[25(cos 240° + i sin 240°)]/[5(cos 60° + i sin 60°)]

I need help setting this up please.

Answer 1

#1
You have
y = 9
x = 9√3
So, tanθ = 1/√3
r = 18
You should be able to recognize a 30-60-90 right triangle...

#2
(4*5)cis(30°+120°)

#3 is just the same.

#4 is the same, but divide r, and subtract angles.