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Prove that if $|z-1-i|=1$, then the locus of a point represented by the complex number $5(z-i)-6$ is a circle with center $(-1,0)$ and radius $5$.

I am not able to get the center coordinates though the radius is quite obvious. Please help.

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2 Answers 2

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HINT

You have $$ 5(z-i)-6 = 5(z-i-1)+5-6=5(z-i-1)-1 $$

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Hint: $w=5(z-i)-6=5(z-1-i)-1 \iff w+1=5(z-1-i)\,$, so $|w-(-1)|=\ldots$

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  • $\begingroup$ Thank you, I was messing up with w+1. $\endgroup$
    – user539746
    Commented Mar 11, 2018 at 19:22

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