Question

How to express z= 1/(1-i) in polar form?

Answer 1

Simplify into a + bi form first

Explanation:

`z = 1/(1-i) = 1/(1-i)*(1+i)/(1+i) = (1+i)/2 = 1/2 + i/2`

Now find `r = | z |`.

`|z| = sqrt(1/4 + 1/4) = sqrt(2/4) = sqrt(2)/2`

In Quadrant 1, `theta = arctan(b/a) = arctan(1) = pi/4`.

Therefore, `z = (sqrt(2)/2)(cos(pi/4) + isin(pi/4))`.