# How do you use DeMoivre's Theorem to find #(1+i)^20# in standard form?

##### 1 Answer

May 19, 2016

#### Answer:

Divide by the norm of

#### Explanation:

De Moivre's formula, which can be derived from Euler's formula that

However, as

#=(sqrt(2))^20(sqrt(2)/2+sqrt(2)/2i)^20#

#=1024(cos(pi/4)+isin(pi/4))^20#

#=1024(cos(20*pi/4)+isin(20*pi/4))#

#=1024(cos(5pi)+isin(5pi))#

#=1024(-1+i*0)#

#=-1024#