Complex Numbers Solutions (1, 2) - Polar Form

The following are the solutions for the problems appearing at the end of the Feb. 28 blog:

(1) We have:


x3 + iy3 = - 4 – i

and: arg(z₃) = arctan(y₃/x₃) = arctan(-1/-4) = arctan(0.25)

so q = arg(z₃) =  14 deg.

The value of r₃= [x₃² + y₃²]^1/2 =  [(-4)² + (-1)²]^1/2 = [17]^1/2 = 4.1

So: z₃ = 4.1 cos(14) + isin(14) = 4.1 cis(14)

(2) Recall: C = z₄ = 4 + 3i

Thence: z₅ = [z₃ + z₄] = [(-4 – i) + (4 – 3i)] = 0 – 4i

arg(z₅) = arctan(y₅/x₅) = arctan(4 /0) = ¥

(No polar form applicable for an infinity)  Cont'd