Why use complex numbers?

Answer 1

One use is to compact a large area into a small one or vice versa. The complex

formula is 1/z, which is inversion. All pairs of complex numbers with absolute value less than 1 will be transformed outside the unit circle and the infinite complex plane will be compacted inside the unit circle! This simple formula produces the real part u=x/(xx+yy) and imaginary part v=-y/(xx+yy). Points approaching infinity will go to zero inside the unit circle!