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math-complex numbers

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Sketch the sets of complex numbers in the complex plane that satisfy the following:
a) |z-1|=2
b) |z-3i|=2
c) |z-5+2i|=2

I'm not sure, but are you supposed to rearrange the whole thing to |z|=a+bi? So, part b would be |z|=2+3i.

  • math-complex numbers - ,

    all are circles of radius 2, with center at various numbers.

    |z-c| = r has center at c.

    |z|^2 = x^2+y^2
    That's why the curves are circles.

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