To find out what type of number results from multiplying \(-8\sqrt{-1}\) (where \(\sqrt{-1}\) represents the imaginary unit \(i\)) and \(\frac{4}{5}\), we can compute the multiplication step by step.
First, let's rewrite \(-8\sqrt{-1}\) as: \[ -8i \]
Now, multiply this by \(\frac{4}{5}\): \[ -8i \cdot \frac{4}{5} = -\frac{32}{5}i \]
This result, \(-\frac{32}{5}i\), is an imaginary number because it includes the imaginary unit \(i\).
Though it has a rational coefficient \(-\frac{32}{5}\), because \(i\) is involved, it is fundamentally an imaginary number.
So, in terms of the provided choices, since the multiplication leads to an imaginary number, it does not correspond to the rational, irrational, or integer classifications.
However, strictly speaking, looking at the nature of the coefficient involving \(i\), the result is most appropriately categorized as:
- neither of the options given (i.e., it is an imaginary number).
Given the choices provided, none exactly match the proper classification. Please double-check your answer options or confirm if you meant a different operation or setup.