SOLUTION: Use de Moivre's Theorem to find the following. Write your answer in standard form. (1 + i)^8

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Question 1007228: Use de Moivre's Theorem to find the following. Write your answer in standard form.
(1 + i)^8
Found 2 solutions by ikleyn, rothauserc:
Answer by ikleyn(52798) (Show Source):
You can put this solution on YOUR website!
.
Use de Moivre's Theorem to find the following. Write your answer in standard form.
(1 + i)^8
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1 + i = .(cos(45�) + i*sin(45�)).

According to de Moivre's Theorem,

= .(cos(8*45�) + i*sin(8*45�)) = .(cos(360�) + i*sin(360�)) = 16.

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
(1 + i)^8
The polar form of (1 + i) = sqrt(2) * (cos(pi/4) + (i * sin(pi/4)))
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complex number = (a + bi)
polar form = r(cos(theta) + i*sin(theta))
consider (1 + i)
r = sqrt(a + b) = sqrt(2) where a = 1 and b = 1
theta is pi/4 since a = 1, b=1, we have an isosceles right triangle
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By de Moivre's Theorem we have
(1 + i)^12 = [sqrt(2) * (cos(pi/4) + (i * sin(pi/4)))]^8 =
(sqrt(2))^8 * (cos(pi/4) + i*sin(pi/4))^8 =
2^4 * (cos(2pi) + i*sin(2pi))
16 * ( 1 + (i * 0) ) =
16