Use the Demoivre's theorem to find the indicated power of the complex number

Question

Express the result in standard form 

(√3+i)^5

Answer 1

z^5 = (√3+i)^5

 

tan(θ) = 1/√(3) => θ = 30° from Special Triangle

 

r = √((√3)^2+1^2) = 2

 

z = 2 e^(i 30°)

 

z^5 = (2 e^(i 30°))^5 = 32 e^(i 150°)

 

z^5 =32(cos(150°) + i sin(150°) )

 

z^5 = 32(-√(3)/2 + 1/2 i) = -16√(3) + 16 i