Question

express in the form of a+ bi​

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

$\frac{ \sqrt{5} + \sqrt{3}i }{ \sqrt{5} - \sqrt{3} i } \\ = \frac{( \sqrt{5} + \sqrt{3} i) {}^{2} }{( \sqrt{5} + \sqrt{3}i)( \sqrt{5} - \sqrt{3}i) } \\ = \frac{5 + 3 + \sqrt{15}i }{5 + 3} \\ = \frac{8 + \sqrt{15}i }{8} \\ = 1 + \frac{ \sqrt{15} }{8} i$

here a=1

b=√15/8