SOLUTION: How do we calculate the real and imaginary parts of (sqrt3 + i)^100 ?
I have tried and my working are as follows:
r = sqrt ((sqrt3)^2 + 1^2) = 2
alpha = arctan (1/sqrt3) = pi/6
Question 470932: How do we calculate the real and imaginary parts of (sqrt3 + i)^100 ?
I have tried and my working are as follows:
r = sqrt ((sqrt3)^2 + 1^2) = 2
alpha = arctan (1/sqrt3) = pi/6
Z = r (cos alpha + i sin alpha)
= 2 (cos pi/6 + i sin pi/6)
= 2 e^i(pi/6)
(sqrt3 + i)^100 = (2e^i(pi/6)^100
= 2^100 x e^i(100pi/6)
= 2^100 x e^i(50pi/3)
= ?
How do I solve from here ? Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! How do we calculate the real and imaginary parts of (sqrt3 + i)^100 ?
I have tried and my working are as follows:
r = sqrt ((sqrt3)^2 + 1^2) = 2
alpha = arctan (1/sqrt3) = pi/6
Z = r (cos alpha + i sin alpha)
Z = 2 (cos pi/6 + i sin pi/6)
For the other 99 roots add 2pi and divide by 600
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= 2 e^i(pi/6)
(sqrt3 + i)^100 = (2e^i(pi/6)^100
= 2^100 x e^i(100pi/6)
= 2^100 x e^i(50pi/3)
