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    Complex Numbers and Analytic Functions

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    Prove algebraically that for complex numbers,
    |z1| - |z2| (is less than or equal to) |z1 + z2| (is less than or equal to) |z1| + |z2|

    Interpret this result in terms of two-dimensional vectors. Prove that
    |z-1| < |sqrt(z^2 - 1) < |z + 1|, for H(z) > 0.

    Show that complex numbers have square roots and that the square roots are contained in the complex plan. What are the square roots of i?

    (See attached for full problem)

    © BrainMass Inc. brainmass.com October 10, 2019, 7:52 am ad1c9bdddf
    https://brainmass.com/math/complex-analysis/complex-numbers-analytic-functions-598464

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    Solution Summary

    The solution illustrates how to show that any complex number has a square root, and how to construct an analytic function.

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