Toronto Math Forum
MAT3342020F => MAT334Lectures & Home Assignments => Chapter 1 => Topic started by: Yifei Hu on September 23, 2020, 11:11:47 AM

Question: let w= 2i , find w^3 + w
Are we suppose to do multiplications directly or are we suppose to use Euler's formula? Since in this case, \theta = arctan(1/2), we can't directly come out the sin and cos of n \theta.
Are there any other alternative methods to apply to such complex numbers with a general arguments that can take advantage of Euler's formula's easy computations of power? Can we give the answer to this question as a polynomial of e^iarctan(c)?

In this case usual cube of the sum would be the most efficient solution