I was told an analytic complex functions has the same derivation value at z0 (random point) however you approach z0. The cauchy riemann eq. shows that z0 has the same derivate value from 2 directions, perpendicular to each other. However, at least some real functions can have the same derivate value in (x0,y0) (random point) approached from 2 directions, without having the same value in another, third direction. So, how does the cauchy riemann eq. prove that its the same from every angle, and not only equal from x and y directions? Hope you understand my question, thnx.