# Toronto Math Forum

## MAT334--2020F => MAT334--Lectures & Home Assignments => Chapter 1 => Topic started by: Yifei Hu on September 23, 2020, 11:11:47 AM

Title: Power of Complex Numbers with Arguments Hard to Determine Directly
Post by: Yifei Hu on September 23, 2020, 11:11:47 AM
Question: let w= 2-i , 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)?
Title: Re: Power of Complex Numbers with Arguments Hard to Determine Directly
Post by: Victor Ivrii on September 24, 2020, 01:34:58 AM
In this case usual cube of the sum would be the most efficient solution