1.

IZ+1ZSo panove thal the pointC1o

Answer»

it forms the general equation of circle

let z = x+iy , then z+1 = (x+1)+iy and z-1 = (x-1)+iy

so |z+1| = √[(x+1)²+y²] and |z-1| = √[(x-1)²+y²]

now squaring both sides..we get

(x+1)²+y² = 2*[(x-1)²-y²] = 2(x-1)²+2y²=> y²-2y² = 2x²+2-4x-x²-2x-1=> x²+y²-6x+1 = 0=> y² + x²-2*(x)*(3) +3³-3³ +1 = 0=> y² +(x-3)²-8 = 0so, y² +(x-3)² = 8... represents a circle.

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