Associated Matrix Arithmetics: How is a Complex Number Associated with a Matrix?

[IrinaK.]

Homework Statement

Hello!
I would be grateful for an explanation of how to proceed with this exercise (see attached). I don't understand what is being asked.

Homework Equations

The Attempt at a Solution

Let's take only multiplication. z*w
I assumed that I have to multiply (a+bi)(c+di) = ac + c(bi) + a(di) + (bi)(di)
If I multiply Z and W, I get what is show on the picture attached.
How does it mirror z*w?

PS I am studying on my own, without teachers, therefore I would be grateful for your patience and help!

 

[qspeechc]

Hi.
It's a badly worded question, I think. First we have to know what the questions means when it says the complex number z is 'associated' with the matrix Z. Can you see how they got the matrix Z from the complex number z?That's what the question means when it says the number z is associated with the matrix Z.

It's easier to start with addition, but since you've done the multiplication we'll start with that. They want you to show how the matrix ZW is associated with the number zw. Let's say V=ZW and v=zw. In your solution you found V=ZW, so now you have to find the number v=zw. Then look at how the number z is associated with the matrix Z, and then look if you can see how v and V are associated.