Express the following expression in the form of a + ib.
\(\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}\)
\(\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}\)
\(=\dfrac{(3^2+(i√5)^2)}{√3+√2i-√3+i√2}\)
\(=\dfrac{9-5i^2}{(2√2i)}\)
\(=\dfrac{9+5}{(2√2i)}×\dfrac{i}{i}\)
\(=\dfrac{14i}{2√2i^2}\)
\(=\dfrac{-7i}{√2}\)
\(=\dfrac{-7i}{√2}×\dfrac{√2}{√2}\)
\(=\dfrac{-7√2i}{2}\) (Ans)