Complex multiplication identity
The formula to convert from the phasor representation \$V=r+jx\$ to its time-domain equivalent is this:

\$
V(t) = Re\{V \, e^{\,j\omega t}\}
\$

Using the complex identity:

\$
e^{\,j\omega t} = \cos(\omega t) + j\,\sin(\omega t)
\$

You obtain:

\begin{align*}
V(t) &amp;= Re\{V \, e^{\,j\omega t}\} 
 = Re\{ (r+jx) \cdot [\cos(\omega t) + j\,\sin(\omega t)] \} = \\[1em]
 &amp;= Re\{ r \cos(\omega t) - x \sin(\omega t) + j[...] \} = \\[1 em]
 &amp;= r \cos(\omega t) - x \sin(\omega t)
\end{align*}