The value of the product [tex](4 - i 2)\cdot (6 + i 2)[/tex] is [tex]z = 28 - i\,4[/tex].
Complex numbers are numbers of the form described below:
[tex]z = a + i\,b[/tex], [tex]a,\,b\in \mathbb{R}[/tex] (1)
Where:
- [tex]i[/tex] - Identification of the complex component.
- [tex]z[/tex] - Identification of the complex number itself.
Let [tex]z_{1}[/tex] and [tex]z_{2}[/tex] be complex numbers, the product of these two complex numbers is also a complex number of the form:
[tex]z_{1} = a + i\,b[/tex] (2)
[tex]z_{2} = c + i\,d[/tex] (3)
[tex]z_{3} = z_{1}\cdot z_{2} = (a + i\,b)\cdot (c + i\,d) = (a\cdot c-b\cdot d) +i\,(a\cdot d + b\cdot c)[/tex]
If we know that [tex]z_{1} = 4-i\,2[/tex] and [tex]z_{2} = 6 + i\,2[/tex], then the product of these two complex numbers is:
[tex]z = (24+4)+i\,(8-12)[/tex]
[tex]z = 28 - i\,4[/tex]
The value of the product [tex](4 - i 2)\cdot (6 + i 2)[/tex] is [tex]z = 28 - i\,4[/tex].
We kindly invite to check this question on complex numbers: https://brainly.com/question/10251853
