+0  
 
0
55
1
avatar

Simplify \[\left( \frac{3 + i \sqrt{3}}{2} \right)^8 + \left( \frac{3 - i \sqrt{3}}{2} \right)^8.\]

 Jan 4, 2021
 #1
avatar
0

We write the complex numbers in exponential form:

 

(2*e^(pi*i/8))^8 + (2*e^(-pi*i/8))^8 = 256*e^(pi*i) + 256*e^(-pi*i) = -512.

 Jan 5, 2021

64 Online Users

avatar
avatar