$$ \begin{alignat}{2} &(0.71+0.71i) \cdot (1000 +100i) \\ = &0.71 \cdot 1000 &+ &0.71 \cdot 100i \\ + &0.71i \cdot 1000 &+ &0.71i \cdot 100i \\ = &710 + 71i + 710i - 71 \\ = & 639 + 781i \end{alignat} $$