Question

Find the product of z1 and z2, where z1 = 2(cos 70° + i sin 70°) and z2 = 4(cos 200° + i sin 200°)

Answer 1

Answer: -8i

2(cos 70 + i sin 70) * 4(cos 200 +isin 200)

8 (cos (70+200) + i sin (70+200)     factor a i sin 70 out

8 (cos(270) + i sin (270))

cos 270 is (0,-1)   sin 270 is -1 from the unit circle

cos 270 is 0

8 (0 -i)

-8i

Answer 2

Answer:

-8i

Step-by-step explanation:

To multiply numbers is polar form

z1 = r1 ( cos theta 1 + i sin theta 1)

z2 = r2 ( cos theta 2 + i sin theta 2)

z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)

z1 = 2(cos 70° + i sin 70°)

z2 = 4(cos 200+ i sin 200)

z1z2 = 2*4 (cos (70+200) + i sin (70+200)

z1z2 = 8 (cos(270) + i sin (270))

       = 8 (0 + i (-1))

       =-8i