Determine the imaginary part of 1 i3123SolutionUsing the fo

Determine the imaginary part of (1 + i*3^1/2)^3

Solution

Using the formula (a+b)^3=a^3+3*a^2*b+3*a*b^2+b^3

(1+i*(3)^1/2)^3=1^3+3*1^2*(3)^1/2+3*1*((3)^1/2)^2+((3)^1/2)^3=1+3((3)^1/2)*i-9-3((3)^1/2)*i=-8

We could see that we\'ve obtained a real number, so the imaginary part is 0.