Question

Express the following expression in the form of a + ib.

$\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}$

Answer 1

$\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}$

$=\dfrac{(3^2+(i√5)^2)}{√3+√2i-√3+i√2}$

$=\dfrac{9-5i^2}{(2√2i)}$

$=\dfrac{9+5}{(2√2i)}×\dfrac{i}{i}$

$=\dfrac{14i}{2√2i^2}$

$=\dfrac{-7i}{√2}$

$=\dfrac{-7i}{√2}×\dfrac{√2}{√2}$

$=\dfrac{-7√2i}{2}$ (Ans)