Operations

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)