4) The roots of the equation z^2+2z+4=0 are denoted by α and β.

Question

a) find α and β in the form re^iθ, giving the values of r and θ
b) Using de Moivre's Theorem, show that α^3=β^3.
c) find the exact value of αβ*+α*β

Answer 1

z = (-2±√-12)/2 = -1±i√3
or 6e^(i 2π/3) and 6e^(i 4π/3)

now the rest is easy...right?