- #1

Juwane

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## Homework Statement

What is the function (linear transformation) that maps [tex]z_{1} = 2[/tex] and [tex]z_{2} = -3i[/tex] onto [tex]w_{1} = 1+i[/tex] and [tex]w_{2} = 3[/tex]?

I think it's asking for the function that if you put 2 in it, it should give 1+i, and if you put -3i in the same function, it should give 3.

The answer given at the back of the book is [tex]w=f(z)=\frac{3+2i}{13}z + \frac{7+9i}{13}[/tex]

## Homework Equations

Maybe these would help:

[tex]x = \frac{z + \overline{z} }{2}[/tex] and [tex]y = \frac{z - \overline{z} }{2i}[/tex]

## The Attempt at a Solution

I have no idea how to even start. The horrible book I am using doesn't give a clue. One possible way is to see what do we have to [tex]z_{1} = 2[/tex] to get [tex]1+i[/tex]. The answer is: [tex]-1+i[/tex] , but we can't add this to [tex]z_{2} = -3i[/tex], since that would give us [tex]1-2i[/tex] whereas we must get 3. Is there any other way to find out?