Find the given power. Write answer in rectangular form.
-$$( 1 + i ) ^ { 20 }$$
A) $- 1024 \mathrm { i }$
B) $- 1024$
C) $1024 \mathrm { i }$
D) 1024

Question

Quizplus · Accepted Answer

The complex number $1 + i$ can be expressed in polar form as $\sqrt{2}(\cos(\pi/4) + i\sin(\pi/4))$. Raising it to the 20th power, we use De Moivre's Theorem: $(\sqrt{2})^{20}(\cos(20\pi/4) + i\sin(20\pi/4)) = 1024(\cos(5\pi) + i\sin(5\pi)) = 1024(-1 + 0i) = -1024$.

Find the Given Power (1+i)20( 1 + i ) ^ { 20 }(1+i)20

Find the Given Power $( 1 + i ) ^ { 20 }$