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Find a mapping between a circle of radius r1 centered at z1 to a circle of radius r2 centered at z2. I thought it would be $w(z)=\frac{r2}{r1}z-z1+z2$ but I was marked wrong. I don't know what I did wrong...

Thanks.

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What you're multiplying by $r_2/r_1$ is the vector from the origin to your point $z$ rather than from the centre of the first circle to $z$.

$(r_2/r_1)(z-z_1) + z_2$ would be correct.

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    Thank you. So I must basically get back to the origin before scaling? Is that the idea here? Is the mapping unique would you say? I was told that it wasn't unique but I am having trouble saying why it isn't... – 2017-02-11
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    No, you went back to the origin when you weren't supposed to. The vector from $z_1$ to $z$ is $z-z_1$. That's what needs to be multiplied by $r_2/r_1$. – 2017-02-11
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    Thank you very much. I think I understand it now. – 2017-02-11