Confused, and there's a test tomorrow.

"write (5+ 2yi) (4-3i)- (5-2yi) (4-31) in a a + bi form, where y is a real number"

  12y +16yi

Step-by-step explanation:

The thing about complex numbers is that you can treat them as binomials and use all of the things you know about multiplying and factoring polynomials.

Here, we assume you have ...

  (5 +2yi)(4 -3i) -(5 -2yi)(4 -3i)

The factor (4 -3i) can be factored out, so you have ...

  = ((5 +2yi) -(5 -2yi))(4 -3i)

  = (4yi)(4 -3i)

  = 16yi -12yi²

At this point, the definition of i comes into play, and you replace i² with -1.

  = 12y +16yi

$5.41

step-by-step explanation:

$20 - $14.51 = $5.49.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).