SECTION 2.3, PAGE 70
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#8. Write both the difference quotient on the left-hand-side and f'(z_0) on the right-hand-side
    in polar form. Then, use the fact that

    lim_{z -> z_0) R e^{i theta) = r e^{i phi) iff R -> r and e^{i theta) -> e^{i phi).
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#11. b) Nowhere analytic since z-bar is nowhere analytic.

     e) x^2 + y^2 = |z|^2 which is differentiable only at z=0. Hence nowhere analytic. 

     g) Nowhere analytic because |z|^2 is differentiable only at z=0.

     h) Nowhere analytic again because |z| is nowhere differentiable.
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