Question

I don't understand. I get an answer that doesn't exist. The question is to multiply in a+bi form. (5/2 + 2i)(1/4 - 6i)

Answer 1

Given the below

`((5)/(2)+2i)((1)/(4)-6i)`

Multiplication of the vectors in the a+bi form gives

Applying the complex arithmetic rule below

`(a+bi)(c+di)=(ac-bd)(ad+bc)i`

The expansion of the vectors gives

`((5)/(2)+2i)((1)/(4)-6i)=(5)/(2)((1)/(4)-6i)+2i((1)/(4)-6i)`

Opening the brackets

`\begin{gathered} ((5)/(2)+2i)((1)/(4)-6i)=(5)/(2)((1)/(4)-6i)+2i((1)/(4)-6i) \\ =(5)/(8)-(30)/(2)i+(2)/(4)i-12i^2 \\ \text{Where i}^2=-1 \\ =(5)/(8)-(30)/(2)i+(2)/(4)i-12(-1) \\ ==(5)/(8)+12-(30)/(2)i+(2)/(4)i \end{gathered}`

Simplifying the above expression

`\begin{gathered} =(5+96)/(8)+(-60i+2i)/(4)=(101)/(8)+(-58)/(4)i \\ =(101)/(8)+(-29)/(2)i=(101)/(8)-(29i)/(2) \\ ((5)/(2)+2i)((1)/(4)-6i)=(101)/(8)-(29i)/(2) \end{gathered}`

Hence, the answer is

`=(101)/(8)-(29i)/(2)`