What is (x+iy-1)((x-iy)-1)=4(x+iy+1)(x-iy+1) ?

The solution to (x+iy-1)((x-iy)-1)=4(x+iy+1)(x-iy+1) is Circle with (a,b)=(-5/3 ,0),r= 4/3

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(x+iy-1)((x-iy)-1)=4(x+iy+1)(x-iy+1)

(x + i y - 1) ((x - i y) - 1) = 4 (x + i y + 1) (x - i y + 1)

(a, b) = (- \frac{5}{3}, 0), r = \frac{4}{3}

Solution steps

(x + i y - 1) (x - i y - 1) = 4 (x + i y + 1) (x - i y + 1)

Rewrite

(x + i y - 1) (x - i y - 1) = 4 (x + i y + 1) (x - i y + 1)

in the form of the standard circle equation

(x - (- \frac{5}{3}))^{2} + (y - 0)^{2} = (\frac{4}{3})^{2}

Therefore the circle properties are:

(a, b) = (- \frac{5}{3}, 0), r = \frac{4}{3}

(x + 3)^{2} + (y - 5)^{2} = 81

(2 x^{2} + 8 x) + (2 y^{2}) + 7 = 0

(x - 5)^{2} + (y - 7)^{2} = 16

(x + 5)^{2} + (y - 3)^{2} = 1

x^{2} + y^{2} = x + 11 y

What is (x+iy-1)((x-iy)-1)=4(x+iy+1)(x-iy+1) ?
The solution to (x+iy-1)((x-iy)-1)=4(x+iy+1)(x-iy+1) is Circle with (a,b)=(-5/3 ,0),r= 4/3