Past exam of the mathematical methods I course of the University of Oxford / 2013 resit / 1 / Solution

Squaring first is simpler than expanding the tenth powers. Since $(1-i{)}^2=-2i$ and $(1+i{)}^2=2i$, while $i^4=1$, the requested Cartesian forms areThus the real part is zero in each case, and the imaginary parts are $-32$ and $32$. The results are complex conjugates, as also follows because the two inputs are complex conjugates and the fifth-power polynomial has real coefficients.