For z1 10cospi3isinpi3 and z2 5cos4pi7isin4pi7 A z1z2 in tri

For z₁= 10(cos(pi/3)+isin(pi/3)) and z₂= 5(cos(4pi/7)+isin(4pi/7))

A) z₁z₂ in trigonometric form

B) z₁z₂ in rectangular form

c) z₁/z₂ in trigonometric form

Solution

a) z1z1 = 10*5 [( cos (pi/3 + 4pi/7) + i sin ( pi/3 + 4pi/7) ]

z1 z2 = 50 [ ( cos 19pi/21 ) + i ( sin 19 pi/21 ) ]

b) rectangular form

50 [ -.955 + .2947 i ]

- 47.75 + 14.735 i

c) z1 / z2 = 10/5 [ ( cos ( pi/3 - 4pi/7 ) + i sin ( pi/3 - 4pi/7 ) ]

z1 / z2 = 2 [ cos ( -5pi/21 ) + i sin ( -5pi/21 ) ]