Trig 7.5: Complex Numbers in Polar Form

θ can also be called...

Argument

The real axis is...

Horizontal

r can also be called...

Modulus

How to convert a complex number from polar to rectangular form?

Solve trig functions (cos and sin) and distribute outside number

The imaginary axis is...

Vertical

a is equivalent to...

rcosθ

b is equivalent to...

rsinθ

Find θ when converting to polar form

tanθ=b/a

If converting an equation like θ=2π/3 into rectangular form...

tanθ=b/a

Rectangular form of a complex number

z=a+bi

Polar form of a complex number

z=r(cosθ+isinθ)

Finding the quotient of a complex number in polar form

z₁/z₂=r₁/r₂[cos(θ₁-θ₂)+isin(θ₁-θ₂)]

Finding the product of a complex number in polar form

z₁z₂=r₁r₂[cos(θ₁+θ₂)+isin(θ₁+θ₂)]

How to find r in z=r(cosθ+isinθ)?

√a²+b²

Used to find the absolute value of a complex number

√a²+b²