### Author Topic: Power of Complex Numbers with Arguments Hard to Determine Directly  (Read 1262 times)

#### Yifei Hu

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##### Power of Complex Numbers with Arguments Hard to Determine Directly
« 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)?

#### Victor Ivrii

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##### Re: Power of Complex Numbers with Arguments Hard to Determine Directly
« Reply #1 on: September 24, 2020, 01:34:58 AM »
In this case usual cube of the sum would be the most efficient solution