Simplify (1 + i√3)^6
We can write [(1 + \sqrt{-3})^6 = (1 + i \sqrt{3})^6.]Let z=1+i3. Then z2=1+2i3+3=4i3, so z3=−3i, and \begin{align*} z^6 &= z^3 z^3 \ &= -3i(-3i) \ &= 9. \end{align*}
Therefore, (1+i*sqrt(3))^6 = 9 .
