Прошу помощи. Деление комплексных чисел. 3i:(3i+1)​

3i:(3i+1)=\dfrac{3i}{3i+1} =\dfrac{3i(3i-1)}{(3i+1)(3i-1)} =\dfrac{9i^2-3i}{(3i)^2-1^2} =

=\dfrac{9i^2-3i}{9i^2-1} =\dfrac{-9-3i}{-9-1}=\dfrac{9+3i}{9+1}=\dfrac{9+3i}{10}=\boxed{\dfrac{9}{10}+\dfrac{3}{10}i}