Question

Find the product of the complex numbers. Express your answer in trigonometric form. z1 = 5(cos(25) + isin(25)) z2 = 2(cos(80) + isin(80))

Answer 1

Z1 = 5(cos25˚+isin25˚)

Z2 = 2(cos80˚+isin80˚)

Z1.Z2 = 5(cos25˚+isin25˚). 2(cos80˚+isin80˚)

Z1.Z2 = 10{(cos25˚cos80˚ + isin25˚cos80˚+i^2sin25˚sin80˚) }

Z1.Z2 =10{(cos25˚cos80˚- sin25˚sin80˚+ i(cos25˚sin80˚+sin25˚cos80˚))}

(i^2 = -1)

Cos(A+B) = cosAcosB – sinAsinB

Sin(A+B) = sinAcosB + cosAsinB

Z1.Z2 = 10(cos(25˚+80˚) +isin(25˚+80˚)

Z1.Z2 = 10(cos105˚+ isin105˚)