Question

Find the polar expression of i and -1

Answer 1

A complex number z=a+ib can be expressed in Cartesian coordinates as (a,b).

To convert to polar coordinates we note that x=rcosθ and y=rsinθ.

The imaginary number i can be represented as (0,1) which means that rcosθ=0 and rsinθ=1, therefore θ=π/2 and r=1, which is (r,θ)=(1,π/2).

The number -1 is (x,y)=(-1,0), so rcosθ=-1 and rsinθ=0, making (r,θ)=(1,π).