Question

If

Answer 1

Answer:

$5 + 2i$

Step-by-step explanation:

We were given the complex numbers;

$a = - 2 - 5i$

and

$b = - i$

We want to find the product;

$a {b}^{3}$

We substitute the complex numbers into the expression and simplify:

$( - 2 - 5i)( {i)}^{3}$

This is rewritten as:

$( - 2 - 5i)( {i)}^{2} \times i$

Note that

${i}^{2} = - 1$

We substitute to obtain:

$( - 2 - 5i) \times - i$Let us expand to get:

$- 2 \times - i + 5i \times - i$

This simplifies to:

$2i - 5 {i}^{2}$

This gives:

$2i - 5( - 1) = 2i + 5$