The 'th root of a complex number

Sunday, 22 April 2018

8:52 PM

Given

If , then  is a root of unity

 

 

• Convert everything to polar form

 

 

 

 

 

 

 

 

If we're given

 

Cartesian form:

 

Polar identity:

 

Polar form - We'll solve that now

Note the  - it is crucial to have this term to allow us to get all the roots

 

Polar form:

 

Equate the polar identity with the polar form

 by de Moivre's theorem

 

Then substitute values of

Ensure that these values are within