Let f: C→C be the function f(2)= wz where @ = u + iv is a fixed complex number. (a) Write down the formula for f viewed as a function f: R² → R², i.e. give formulas for Re(f) and Im(f) in terms of x = Re(z) and y = Im(z). (b) Compute the total derivative Df of fat z as a 2 by 2 matrix with real entries. (c) Describe the linear transformation of the plane determined by this matrix and relate it to the complex number .

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