Consider complex numbers z = 1 +j, w = −1 + j, v = −1 − j, and u = 1 − j. You may use MATLAB compass to plot vectors corresponding to complex numbers to verify your analytic results.

(a) In the complex plane, indicate the point (x, y) that corresponds to z and then show a vector ­z that joins the point (x, y) to the origin. What is the magnitude and the angle corresponding to z or ­Vector z?

(b) Do the same for the complex numbers w, v, and u. Plot the four complex numbers and find their sum z + w + v + uanalytically and graphically.

(c) Find the ratios z/w, w/v, and u/z. Determine the real and imaginary parts of each, as well as their magnitudes and phases. Using the ratios find u/w.

(d) The phase of a complex number is only significant when the magnitude of the complex number is significant. Consider z and y = 10⁻¹⁶z, compare their magnitudes and phases. What would you say about the phase of y?