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
(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 ...
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.