Question

How do you find the center or |z-1|=1?

|Z|=|x+yi|=sqrt(x^2+y^2)
The answer is suppose to be (1,0)

Answer 1

that says the distance between \(z\) and 1 is 1

Answer 2

all points in the complex plane whose distance from 1 is 1 unit , so a circle

Answer 3

you need some kind of algebra method?

Answer 4

if \(z=a+bi\) then \(z-1=(a-1)+bi\) and so \[|(a-1)+bi|=\sqrt{(a-1)^2+b^2}=1\]

Answer 5

Oh I see, thank you so much!

Answer 6

or in your notation \[(x-1)^2+y^2=1\] a circle with center \((1,0)\) and radius 1
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