Find the value of

Question

if z=1/2 (i√3-1) , then find the value of (z -z² +2z³) x (2-z+z²) is ?

Answer 1

Given z=1/2 (i√3-1)

=>z²=1/4 (i√3-1)²

        =1/4(-3-2√3i+1)

        = -1/4×2(√3i+1)

       = -1/2(√3i+1)

So    z³=z²×z=-1/2(√3i+1)x1/2 (√3i-1)= -1/4(-3-1)=1

Now

(z -z² +2z3) x (2-z+z²)

=(z -z² +2.1) x (2-z+z²)

=(2 -z² +z) x (2-z+z²)

={2 -(z²-z)} {2 +(z²-z)}

=4-(z⁴-2z³+z²)

=4-(z-2+z²)

=4-(1/2 (i√3-1)-2-1/2(√3i+1)

=4-(-1/2 -2-1/2)

=4-(-1-2)=4+3=7