Tuesday, January 9, 2018

complex numbers - If $left| frac{z-i}{z-1}right| = sqrt2$ and $|z| = sqrt 5$ and $Im(z)

I'm having a lot of problem with the first term. If I try to rationalize the fraction, I get an expression too long to work with. Similarly, substituting from the second term gives horrible results.



Breaking the modulus apart and squaring gives me an incorrect result, and I just don't know how to approach the problem anymore. I'm probably making a dumb mistake along the lines, but I'd be grateful if someone could solve this step by step.



EDIT: Wrote the thing incorrectly, switched the denominator and enumerator. Sorry for anyone who solved the wrong thing, but they should be similar enough for a simple switch, no?

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