Past exam of the mathematical methods I course of the University of Oxford / 2014 resit / 1 / ii

The polar form $1+i=\sqrt{2}{e}^{i\pi /4}$ gives $(1+i{)}^6=-8i$. Multiplication therefore scales the modulus by $8$ and rotates the complex argument through $-\pi /2$:Equivalently the result is $8b-8ia$, whose complex argument is $atan2(-a,b)$. If $a=b=0$, its modulus is zero and its complex argument is undefined.