Can someone answer this complex number question

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\ (| z-1 | <| z + i | \) <=> \ (| (x-1) + iy | ^ 2 <| x + i (y + 1) | ^ 2 \) <=> \ ((x-1) ^ 2 + y ^ 2 \ (-x

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gerdware
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Hi Revan,

I think it would be clearer to write the complex numbers as 2-dimensional vectors (then the amount is simply the Euclidean norm :-)).
With that you could easily calculate the right and left side.

Do you know what 1 and i look like as a complex number or as 2-dimensional vectors?

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jannine
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I would square the equation and use the formula for the amount, it says above. With \ (z = a + b \, i \) the inequality then reads: \ ((a-1) ^ 2 + b ^ 2