Find the product of these complex numbers.
(2-3i) * (1 - i) =

- 1 - 5i

Step-by-step explanation:

note that i² = - 1

Given

(2 - 3i)(1 - i) ← expand using FOIL

= 2 - 2i - 3i + 3i²

= 2 - 5i - 3

= - 1 - 5i

-1 - 5i

Step-by-step explanation: It's important to understand that we

can work this problem as if we were multiplying two binomials together.

In other words, we can use the F.O.I.L. method. First, Outer, Inner, Last.

The product of the first terms in each complex number is 2.

The product of the outer terms is -2i.

The product of the inner terms is -3i.

The product of the last terms is 3i².

Next, we combine our like terms. So -2i + -3i = -5i.

Also, i² is -1 so our last term is just 3(-1) or -3.

So we have 2 - 5i + (-3) or 2 - 5i - 3 which is -1 - 5i.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

$54.99

step-by-step explanation:

$54.99 includes 500 min. if she does not exceed 500 min then her bill is $54.99