Medium Practice — Set 1

Quick Recap — Complex Numbers (Polar, De Moivre, $\omega$)

• Polar form: $z=r(\cos\theta+i\sin\theta)$, $r=|z|$, $\theta=\arg z$.
• De Moivre: $(\cos\theta+i\sin\theta)^n=\cos n\theta+i\sin n\theta$.
• Cube roots of unity $1,\omega,\omega^2$: $\omega^3=1$, $1+\omega+\omega^2=0$, $\bar\omega=\omega^2$.
• $|z_1z_2|=|z_1||z_2|$; the $n$ $n$-th roots of unity sum to $0$.