Complex numbers, locus

Question

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.

Answer 1

HINT

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

Answer 2

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