Find the product of z =(cos 60°+i sin 60°) and z2 = 9(cos 20° +i sin 20°) where Ose < 360°. 122 = 9.67 cis 80° 2122 = 6 cis 80° %3D 2123 = 6cis40° 2 2122 = cis 40° 27
To find the product of z and z2, we simply multiply their magnitudes and add their angles:
z = cos 60° + i sin 60°
|z| = √(cos^2(60°) + sin^2(60°)) = √(1/4 + 3/4) = 1
arg(z) = 60°
z2 = 9(cos 20° + i sin 20°)
|z2| = 9
arg(z2) = 20°
|z * z2| = |z| * |z2| = 1 * 9 = 9
arg(z * z2) = arg(z) + arg(z2) = 60° + 20° = 80°
Therefore, the product of z and z2 is 9(cos 80° + i sin 80°), which can be written as 9 cis 80°.