Think of $z$ not just as a complex number here, but as a vector with a magnitude and a direction undergoing two transformations to become vector $v$; first $z$ is being dilated by length 3, and then being translated rightward by length 2. The locus of $v$ such that their magnitude is less than length of 1 is easier to visualize, and you can work backwards from there. – 2011-02-15
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Thank you. That way to analyze the problem made me think better – 2011-02-15
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Try to think of it as a ball centered at a point. bring a 3 over to the other side and you will see what the center and radius are. – 2011-02-15
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Hint: How do you find the modulus of a complex number?