Question

Express the following division in the form of a + bi: (1+3i)(2+i)

Answer 1

`(1 + i\,3) \cdot (2 + i) = -1 + i\,7`

Explanation:

We proceed to present the procedure by algebraic means:

1)
`(1 + i\,3)\cdot (2 + i)` Given

2)
`2\cdot (1 + i\,3) + i\,(1+i\,3)` Distributive and Commutative Properties

3)
`2 + i\,6 + i + i^(2) \,3` Distributive, Commutative and Associative Properties

4)
`2 + i\,7 -3` Definition of imaginary number/Distributive, Commutative and Associative Properties

5)
`-1 + i\,7` Commutative and Associative Properties