Calculate z/w, write the answer in trigonometric form.

Question

Calculate z/w if z = 32(cos(pi) + i sin(pi)) and w = 4(cos(3pi/5) + i sin(3pi/5)) write the answer in trigonometric form. Simplify

Answer 1

To divide complex numbers in polar form, divide the magnitudes and subtract the angles.

So, if z = 32(cosπ + isinπ) and w = 4(cos(3π/5) + isin(3π/5)), then

z/w = (32/4)[cos(π-3π/5) + isin(π-3π/5)]

Simplify!