Find each product in rectangular form using exact values 57

Find each product in rectangular form, using exact values. 57. [ 3(cos 60degree + i sin 60degree) ] [2(cos 90degree + i sin 90degree) ] 59. [ 2(cos 45degree + i sin 45degree) ] [2(cos 225degree + i sin 225degree) ] 58. [ 4(cos 30degree + i sin 30degree)] [5(cos 120degree + i sin 120degree)] 60. [ 8(cos 300degree + i sin 300degree) ] [ 5 (cos 120degree + is in 120degree)] 61.[5cis pi/2][3 cis pi/4] 62. [6 cis 2pi/3][[5 cis(-pi/6)]

Solution

62 [ 6cis(2pi/3)][5cis(-pi/6)]

take the product the modulus part = 6*5 = 30

add the angles = 2pi/3 -pi/6 = 3pi/6 = pi/2

Now [ 6cis(2pi/3)][5cis(-pi/6)] = 30cis(pi/2)

= 30[ cospi/2 +i*sinpi/2]

= 30*i

=30i