HOW TO FIND CUBE ROOT OF A GIVEN NUMBER

Problem 1 :

Solution:

The given number is in polar form.

Problem 2 :

The complex fifth roots of 32.

Solution:

n^th roots of z = r cis θ

Problem 3 :

The complex sixth roots of 64.

Solution:

Problem 4 :

The complex cube roots of 1.

Solution:

z³ = 1

Let z = x + iy

(x + iy)³ = 1

z = r(cis θ) 

= cis 0 

= cis(0 + 2kπ) 

= cis(2kπ) 

Problem 5 :

The complex cube roots of i.

Solution:

Problem 6 :

The complex fourth roots of 1 + i

Solution: 

Problem 7 :

The complex fifth roots of -1 + i

Solution: