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

Name: Find the given power. Write answer in rectangular form. -\[( 1 + i ) ^ { 20 }\] A) 1024 B) 1024i C) -1024i D) -1024
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Question

Quizplus · Accepted Answer

The complex number $1 + i$ has a magnitude of $\sqrt{2}$ and an angle of $\frac{\pi}{4}$. Raising it to the 20th power gives a magnitude of $2^{10} = 1024$ and an angle of $5\pi$, which corresponds to the real part being $-1024$ and the imaginary part being 0.

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

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