Question

Please help simplify and write your answer in the form a + bi

Answer 1

`2 - 4i`

Explanation:

`(10)/(1 + 2i) \\ \\ = (10)/(1 + 2i) * (1 - 2i)/(1 - 2i) \\ \\ = \frac{10(1 - 2i)}{ {1}^(2) - {(2i)}^(2) } \\ \\ = \frac{10 - 20i}{ {1} - {4i}^(2) } \\ \\ = \frac{10 - 20i}{ {1} - {4( - 1)} } \\ ( \because \: {i}^(2) = - 1) \\ \\ = (10 - 20i)/(1 + 4) \\ \\ = (5(2 - 4i))/(5) \\ \\ = 2 - 4i`