FIND THE INDICATED ROOTS OF THE COMPLEX NUMBER IN POLAR FORM

Find all the complex roots. Write roots in polar form with θ in degrees.

Problem 1 :

The complex square roots of 9(cos 30° + i sin 30°)

Solution:

Let z = 9(cos 30° + i sin 30°)

The given number is in polar form.

Problem 2 :

The complex square roots of 25 (cos 210° + i sin 210°)

Solution:

Let z = 25(cos 210° + i sin 210°)

The given number is in polar form.

Problem 3 :

The complex cube roots of 8(cos 210° + i sin 210°)

Solution:

Let z = 8(cos 210° + i sin 210°)

The given number is in polar form.

Problem 4 :

The complex cube roots of 27(cos 306° + i sin 306°)

Solution:

Let z = 27(cos 306° + i sin 306°)

The given number is in polar form.

Find all the complex roots. Write roots in rectangular form. If necessary, round to the nearest tenth.

Problem 5 :

Solution:

The given number is in polar form.