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) = p

Question 470931: 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!
duplicate
RELATED QUESTIONS
How do we calculate the real and imaginary parts of (sqrt3 + i)^100 ? I have tried and... (answered by Alan3354)

ALRIGHT. SO THE PROBLEM IS WRITTEN AS FOLLOWS: {{{ 3*sqrt(-75)+5*sqrt(-48) }}} PERFORM... (answered by RAY100)

sqrt75 - sqrt12 + sqrt3 = 5 sqrt3 - 2 sqrt3 + sqrt3 = 3 sqrt3 i just want to know if... (answered by rapaljer)

Please help me rationalize denominator and numerator {{{... (answered by stanbon)

I am supposed to find the imaginary solution to the following equation and check my... (answered by anjulasahay)

I need to know if my answers are correct. I am to classify each of the problems as real... (answered by stanbon)

Q. If {{{a = sqrt(3) + sqrt(5)}}} ; b={{{sqrt(sqrt(3)+sqrt(5))}}} and {{{r=a/b}}}, then... (answered by rothauserc)

What is the final solution for: (3-sqrt(-7))+(5+sqrt(-2)) I know you have to put it (answered by solver91311)

if i have for example - sqrt 25/12 = sqrt25 is 5 and sqrt 12 would be sqrt 4 times sqrt 3 (answered by Earlsdon)