contestada

If
a=−2−5ia=-2-5i
a=−2−5i and
b=−ib=-i
b=−i, then find the value of the
ab3ab^3
ab
3
in fully simplified form.

Respuesta :

kudzordzifrancis

Answer:

[tex]5 + 2i[/tex]

Step-by-step explanation:

We were given the complex numbers;

[tex]a = - 2 - 5i[/tex]

and

[tex]b = - i[/tex]

We want to find the product;

[tex]a {b}^{3} [/tex]

We substitute the complex numbers into the expression and simplify:

[tex]( - 2 - 5i)( {i)}^{3} [/tex]

This is rewritten as:

[tex]( - 2 - 5i)( {i)}^{2} \times i[/tex]

Note that

[tex] {i}^{2} = - 1[/tex]

We substitute to obtain:

[tex]( - 2 - 5i) \times - i [/tex]Let us expand to get:

[tex] - 2 \times - i + 5i \times - i[/tex]

This simplifies to:

[tex]2i - 5 {i}^{2} [/tex]

This gives:

[tex]2i - 5( - 1) = 2i + 5[/tex]

facundo3141592

The product of the complex numbers will be:

a*b^3 =  -2i*b^3 + 5b^3

How to find the given expression?

We know that:

  • a = -2 - 5i
  • b = -ib

Then the product of the complex numers is:

a*b^3 = (-2 - 5i)*(-ib)^3

Remember that i^2 = -1, then:

a*b^3 = (-2 - 5i)*(-ib)^3 = (-2 - 5i)*(-ib)^2*(-ib)

                                    = (-2 - 5i)*(-b^2)*(-ib) = (-2 - 5i)*(ib^3)

                                    = -2i*b^3 + 5b^3

If you want to learn more about complex numbers, you can read:

https://brainly.com/question/10662770