Manipulating complex numbers Express the complex number $(-1-i)^{48}(-3+i\sqrt{3})^{36}$ in the form a + bi?
I got $ (2^{24})(12^{18}) + 0i $?
Did I get it right?

Note: $\:x\: =\: -1\:-\:i\: \Rightarrow\:x^4 = (2i)^2 =\: -4.\ $ Recall $\:\zeta^3 = 1\:$ for $\:\zeta = (-1 - \sqrt{-3})/2\:$
thus $\:y\: =\:  \sqrt{-3} - 3\ \Rightarrow\: y^6 \: =\: \left(\sqrt{-3}\: (1+\sqrt{-3})\right)^6\ =\ (\sqrt{-3}\:(-2\:\zeta))^6 \:=\: - 2^6\cdot 3^3$
Therefore $\:x^{48} y^{36} = (x^8 y^6)^6 = (2^4\: (-2^6\cdot 3^3))^6 =\: 2^{60} 3^{18}$
