Consider f(x)=z-2z^2. identify the real and imaginary parts of f

Suppose that the function f(z) = u(x,y) + iu(x,y) is analytic in some domain D. we can define two families of curves in D. The equations u(x, y) = q and v(x,y) = c2, where c1 and c2 are arbitrary constants, define the level curves of u and v. These level curves form orthogonal families, i.e. each curve in one family is orthogonal to each curve in the other family. Consider f(z) 222 1. Identify the the real and imaginary parts of f, i.e. the functions u(r, y) and v(x, y). and u(x, y) = c2. given curve, and the Cauchy-Riemann equations, to show that the two 2. Using implicit differentiation, como family u(.) 3. Use the fact that represents the slope of the tangent line to the families of curves are orthogonal.