Find The Product Of The Complex Numbers. Express Your Answer In Trigonometric Form

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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))


solution: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 – sinAsinBSin(A+B) = sinAcosB + cosAsinBZ1.Z2 = 10(cos(25˚+80˚) +isin(25˚+80˚)  Z1.Z2     = 10(cos105˚+ isin105˚)

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