Question

Simplify and write your answer in the form a+bi.

Answer 1

$\dfrac{10}{1+2i}\\\\\\=\dfrac{10(1-2i)}{(1+2i)(1-2i)}\\\\\\=\dfrac{10-20i}{1 - (2i)^2}\\\\\\=\dfrac{10-20i}{1+4}~~~~~;[i^2 =-1]\\\\\\=\dfrac{10-20i}5\\\\=\dfrac{10}5 - \dfrac{20i}5\\\\=2-4i$