how do you convert 1 - i to polar form
First, let's find r. This is given by r = lzl = SQRT(a^2 + b^2) = SQRT(1^2 + (-1)^2) = SQRT (2)
Now, let us find θ. We have tan θ = b/a = -1 / 1. Note that this is just a 45 degree angle in the 4th quadrant, i.e., [ -(pi) / 4]
And the polar form is given by
z = r (cos θ + i sin θ) =
√(2) (cos [ -(pi) / 4] + i sin [ -(pi) / 4])
Note one thing here...For completeness sake, any value of [ -(pi) / 4] + 2* pi *n where n is a positive or negative integer would work since all these angles would give the same answer !!!