Question

Simplify:

$(1+\frac{2}{i})(3+\frac{4}{i})(5+i{)}^{-1}$

Answer 1

$(1+\frac{2}{i})(3+\frac{4}{i}){(5+i)}^{-1}(1-2i)(3-4i)\left(\frac{1}{5+i}\right)(3-2i-4i-8)\left(\frac{5-i}{25+1}\right)\frac{(-5-6i)(5-i)}{26}\frac{-25-30i+5i-6}{26}\frac{-31-25i}{26}$