![5 + 2i](/tpl/images/0560/7704/11bfa.png)
Step-by-step explanation:
We were given the complex numbers;
![a = - 2 - 5i](/tpl/images/0560/7704/657e3.png)
and
![b = - i](/tpl/images/0560/7704/02d9e.png)
We want to find the product;
![a {b}^{3}](/tpl/images/0560/7704/79d6b.png)
We substitute the complex numbers into the expression and simplify:
![( - 2 - 5i)( {i)}^{3}](/tpl/images/0560/7704/6924e.png)
This is rewritten as:
![( - 2 - 5i)( {i)}^{2} \times i](/tpl/images/0560/7704/b037e.png)
Note that
![{i}^{2} = - 1](/tpl/images/0560/7704/87b08.png)
We substitute to obtain:
Let us expand to get:
![- 2 \times - i + 5i \times - i](/tpl/images/0560/7704/aa995.png)
This simplifies to:
![2i - 5 {i}^{2}](/tpl/images/0560/7704/c8e90.png)
This gives:
![2i - 5( - 1) = 2i + 5](/tpl/images/0560/7704/ece75.png)