Module 8 Quiz: Polar Coordinates & Complex Numbers
Final Module Quiz
10 questions. Aim for 7+ correct!
1
Convert (4, π/6) to rectangular.
(4cos(π/6), 4sin(π/6)) = (2√3, 2).
2
Convert (3, 3) to polar.
r=3√2, θ=π/4. (3√2, π/4).
3
x = rcosθ, y = ?
y = r sinθ
4
Rose r=2sin(3θ): how many petals?
3 (n=3, odd).
5
r=3+3cosθ is what type of curve?
Cardioid (a=b=3).
6
Write z=2+2i in trig form.
r=2√2, θ=π/4. 2√2(cos(π/4)+isin(π/4)).
7
State DeMoivre's Theorem.
[r(cosθ+isinθ)]n = rn(cos nθ + i sin nθ).
8
How many cube roots does a nonzero complex number have?
3.
9
Convert r=5 to rectangular.
x²+y²=25.
10
Multiply: 3(cos40+isin40) times 2(cos50+isin50).
6(cos90+isin90) = 6i.