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    Solutions of relations on the complex numbers

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    Sketch the sets of points determined by the following relations:

    a) Re(z + 1) = 0

    b) Im(z - 2 i) > 6.

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    https://brainmass.com/math/complex-analysis/solutions-relations-complex-numbers-525249

    Solution Preview

    (a) Let z = x + iy, where x and y are real numbers (i.e., x = Re(z) and y = Im(z)).

    Substituting x + iy for z (in z + 1), we obtain z + 1 = (x + iy) + 1.

    Combining the two terms that consist of real numbers (namely, x and 1), we get (x + iy) + 1 = (x + 1) + iy.

    Thus z + 1 = (x + 1) + iy, hence Re(z + 1) = x + 1.

    To solve the equation Re(z + 1) = 0, we set x + 1 to 0 and solve ...

    Solution Summary

    Two relations (one equation and one inequality) are given on the complex numbers. Their solutions are derived, and detailed explanations of the solutions are provided.

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