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T(x + yi) = x - yi

Show that this is a linear transformation and find the matrix of the transformation using the following basis

(1+i, 1-i)

ARGH

I am having trouble with the complex numbers for some reason!

To show that it is linear I have to show

T(x + yi + a + bi) = x + (-yi) + a + (-bi) = x + a + (- i(y +b)) = T(x + yi + a +bi) = x + (-yi) + a + (-bi)

T(k(x + yi)) = k(x + (-yi)) = kx + k(-yi) = T(k(x + (-yi)) = kT(x + (-yi))

Is this correct?

And as for finding the matrix. OY!

I know B = [ [T(1+i)] [T(1-i)] ]

So I know how to do it in theory, kind of I guess. But I just don't know how to start :/

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# Linear Transformations and their matrices

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