If z =x+ iy is a complex number, then the equation | z +i z -i |= 3 represents the

Step-by-step solution

Given the equation | z+i z-i |= 3 , substitute z=x+iy to obtain: | x+i(y+1) x+i(y-1) |= 3 . Applying the modulus property | z₁ z₂ |= |z₁| |z₂| and squaring both sides yields: x^2+(y+1)^2 x^2+(y-1)^2 =3 . Multiplying through by the denominator and expanding gives: x^2+y^2+2y+1=3x^2+3y^2-6y+3 . Rearranging terms and simplifying leads to: 2x^2+2y^2-8y+2=0 , which reduces to x^2+y^2-4y+1=0 after division by 2. Completing the square for y results in: x^2+(y-2)^2=3 . This represents a circle centered at (0,2) with radius