Explore BrainMass

Explore BrainMass

    Solutions of relations on the complex numbers

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Sketch the sets of points determined by the following relations:

    a) Re(z + 1) = 0

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

    © BrainMass Inc. brainmass.com March 5, 2021, 12:41 am ad1c9bdddf
    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.

    $2.49

    ADVERTISEMENT