Question

Find all the complex cube roots of w = 125( cos 240° + i sin 240°). Write the roots in polar form with θ in degrees.

Z0 = __(cos__°+ i sin __°

Answer 1

To find the complex cube roots of w = 125(cos 240° + i sin 240°), we can rewrite it in polar form as w = 125∠240°. The cube roots of w can be found by taking the cube roots of the magnitude and dividing the argument by 3. So, the complex cube roots are Z₀ = 5∠80°, Z₁ = 5∠160°, and Z₂ = 5∠240°.

Step-by-step explanation:

To find the complex cube roots of w = 125(cos 240° + i sin 240°), we can rewrite it in polar form as w = 125∠240°.

The cube roots of w can be found by taking the cube roots of the magnitude and dividing the argument by 3.

So, the complex cube roots are:

1. Z₀ = 5∠80°
2. Z₁ = 5∠160°
3. Z₂ = 5∠240°