Phantom graphs use the 3D graphing capability of GeoGebra to show all solutions, both real and complex, to many equations. In general, they will show all solutions to f(x)=c where c ranges over all reals. Explore to find that by extending to complex numbers we can graph the solutions to x^2=-4 and even see that cos(z)=7 actually has a complex solution (an infinite number of them). In all the applets in this book if the point A(a, b, c) is on the phantom graph, then letting x=a+ic and y=b will give values that satisfy the original equation. Note that y=b is the middle value since we are using the x-axis as real and the z-axis as the imaginary axis.
