(2+2i)^4/(1-√3i)^5=[(2^4)(1+i)^4]/[(-2)(-1/2+√3/2i)]^5=[(2^4)(2i)^2]/[(-2^5)(-1/2+√3/2i)^2]=-64/[(-32)(-1/2-√3/2i)]=2/(-1/2-√3/2i)=-4/(1+√3i)=-4(1-√3i)/4=-1+√3i