3.13-3.15

Rectangular Form

z = a + bi

Trigonmetric From (Polar Form)

z = r(cosθ + isinθ)

How to find a

= rcosθ

Average Rate of Change of a Polar Function

f(b)-f(a)/b-a

How to find b

= rsinθ

How to find r

= √a²+b²

tanθ=

b/a

How do I put complex numbers (polar form) in rectangular form?

Turn the cosθ into one number, multiple radius to both numbers

Polar Coordinates

Uses distance and angles

Polar Scis

An initial ray from the role, usually horizontal and to the right

Polar Coordinates

In the form (r, θ), where r is the directed distance from the pole to the point, and θ is the directed angle.

When converting the polar equations to rectangular, all you have to do is

Replace a with x and b with y

Cardiod

If a=b

Outlook = 2a

If r=f(cos)

Symmetric with the polar axis (meaning x-axis)

If r=f(sin)

Symmetric with the line θ=π/2 (y-axis)

Roses

a•sin(nθ)

a•cos(nθ)

n→even→2n petal

n→odd→ n petal

Looped Limacon

a<b

Outlook a+b

Inner loop b-a

The distance between r=f(θ) and the origin is increasing

1. r=f(θ) is positive and increasing

2. r=f(θ) is negative and decreasing

The distance between r=f(θ) and the origin is decreasing

1. r=f(θ) is positive and decreasing

2. r=f(θ) is negative and increasing