Question

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"

Answer 1

12y +16yi

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