What is the product of 4 [cos(2pi/3) +i sin(2pi/3)] and 2 [cos(pi/3) + i sin (pi/3)].

Question

asked Apr 26, 2023 152k views

2 Answers

Ivan Dal Bosco · Answer 1 · 2023-05-01T13:52:50+0000

When multiplying two complex numbers in polar form, all you need to do is multiply the moduli and sum the arguments. Let

z = 4 (cos(2π/3) + i sin(2π/3))

w = 2 (cos(π/3) + i sin(π/3))

Then

|z| = 4

arg(z) = 2π/3

|w| = 2

arg(w) = π/3

and so

zw = |z| |w| (cos(arg(z) + arg(w)) + i sin(arg(z) + arg(w)))

zw = 8 (cos(π) + i sin(π))

zw = -8