Imaginary curve

For example, the set of pairs of complex numbers ${\displaystyle (x,y)}$ satisfying the equation ${\displaystyle x^{2}+y^{2}=-1}$ forms an imaginary circle, containing points such as ${\displaystyle (i,0)}$ and ${\displaystyle ({\frac {5i}{3}},{\frac {4}{3}})}$ but not containing any points both of whose coordinates are real.