From Förberedande kurs i matematik 2

Complex numbers satisfy the same rules of arithmetic as ordinary numbers, with the addition that \displaystyle i^2=-1. The distributivity rule gives that

\displaystyle \begin{align} i(2+3i) &= i\cdot 2 + i\cdot 3i\\[5pt] &= 2i+3i^2\\[5pt] &= 2i+3\cdot (-1)\\[5pt] &= 2i-3\\[5pt] &= -3+2i\,\textrm{.} \end{align}