Polar and Parametric Equations

Question 1

complex equations –> rectangular form

Answer 1

a + bi

Question 2

complex equations –> polar form

Answer 2

r(cosθ + isinθ)

Question 3

coordinates –> rectangular form

Answer 3

(x, y)
(rcosθ, rsinθ)

Question 4

coordinates –> polar form

Answer 4

(r, θ)

Question 5

product of complex numbers (polar form)

Answer 5

z1z2 = r1r2(cos(θ1 + θ2) + isin(θ1 + θ2))

Question 6

quotient of complex numbers

Answer 6

z1/z2 = r1/r2 * (cos(θ1 - θ1) + isin(θ1 - θ2))

Question 7

de Moivre’s Theorem

Answer 7

z^n = r^n(cos(nθ) + isin(nθ))

Question 8

parametric equations

Answer 8

x = t
y = t

Question 9

eliminating the parameter

Answer 9

y = m(x - x1) + y1
r^2 = (x-h)^2 + (y-k)^2

Question 10

converting between polar and rectangular form

Answer 10

x^2 + y^2 = r^2
rcosθ = x
rsinθ = y

Question 11

θ = a

Answer 11

graph is straight line

Question 12

r = a

Answer 12

graph is circle centered at origin
a = diameter

Question 13

r = acosθ

Answer 13

graph is circle shifted horizontally
a = diameter

Question 14

r = asinθ

Answer 14

graph is circle shifted vertically
a = diameter

Question 15

r = acos(nθ) or r = asin(nθ)

Answer 15

graph is rose-shaped
if n is odd: n number of petals
if n is even: 2n number of petals
(2π)/(number of petals) = angle distance between tips of petals