The document discusses operations with complex numbers in polar form. It provides the polar form representations of two complex numbers z1 and z2 as r1(cosθ1 + i sin θ1) and r2(cosθ2 + i sin θ2). It asks the reader to find the product and quotient of z1 and z2 using the polar form, and notes that the product can also be expressed as r1 cisθ1 × r2 cisθ2. It provides hints about using trigonometric addition formulas to simplify the expressions and concludes with two practice problems asking the reader to find the product and quotient of complex numbers given in polar form.

1. 1
Operations with Complex Numbers in Polar Form
Let 𝑧! = 𝑟!(𝑐𝑜𝑠𝜃! + 𝑖 sin 𝜃!) and 𝑧! = 𝑟!(𝑐𝑜𝑠𝜃! + 𝑖 sin 𝜃!)
a) Find 𝑧! 𝑧!
(this can also be expressed as 𝑟! 𝑐𝑖𝑠𝜃!×𝑟! 𝑐𝑖𝑠𝜃!)
b) Find
!!
!!
What can you conclude about:
𝑧! 𝑧!
arg (𝑧! 𝑧!)
In Euler Form:
𝑟! 𝑒!!!
𝑟! 𝑒!!!
=
!!!!!!
!!!!!! =
Hint remember your addition formulae:
cos(𝜃! + 𝜃!) = 𝑐𝑜𝑠𝜃! 𝑐𝑜𝑠𝜃! − 𝑠𝑖𝑛𝜃! 𝑠𝑖𝑛𝜃!
sin (𝜃! + 𝜃!) = 𝑠𝑖𝑛𝜃! 𝑐𝑜𝑠𝜃! + 𝑐𝑜𝑠 𝜃! 𝑠𝑖𝑛𝜃!
Hint:
!!!"#!!
!!!"#!!
×
!"#(!!!)
!"#(!!!)

2. 2
Practice
1) Find 𝑧! 𝑧!
When 𝑧! = 3𝑐𝑖𝑠
!!
!
𝑎𝑛𝑑 𝑧! = 4𝑐𝑖𝑠
!
!
2)