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Solution: Edit and execute the following script M-file:

N=10;
n=1:N;
amplituden=1./n;
phasen=n.^2;
phasorn=amplituden.*exp(j.*phasen);
phasortot=sum(phasorn);
amplitudetot=abs(phasortot)
phasetot=angle(phasortot)

In-Class Exercises

Pb. 6.36 Could you have estimated the answer to Example 6.8? Justify your
reasoning.
Pb. 6.37 Show that if you add N signals with the same magnitude and fre-
quency but with phases equally distributed over the [0, 2π] interval, the
resultant phasor will be zero. (Hint: Remember the result for the sum of the
roots of unity.)
Pb. 6.38 Show that the resultant signal from adding N signals having the
same frequency has the largest amplitude when all the individual signals are
in phase (this situation is referred to as maximal constructive interference).
Pb. 6.39 In this problem, we consider what happens if the frequency and
amplitude of N different signals are still equal, but the different phases of the
signals are randomly distributed over the [0, 2π] interval. Find the amplitude
of the resultant signal if N = 1000, and compare it with the maximal construc-
tive interference result. (Hint: Recall that the rand(1,N) command gener-
ates a 1-D array of N random numbers from the interval [0, 1].)
Pb. 6.40 The service provided to your home by the electric utility company
is a two-phase service. This means that two 110-V/60-Hz hot lines plus a neu-
tral (ground) line terminate in your panel. The hot lines are π out of phase.
a. Which signal would you use to drive your clock radio or your
toaster?
b. What configuration will you use to drive your oven or your dryer?
Pb. 6.41 In most industrial environments, electric power is delivered in
what is called a three-phase service. This consists of three 110-V/60-Hz lines
with phases given by (0, 2π/3, 4π/3). What is the maximum voltage that you
can obtain from any combination of two of these signals?
Pb. 6.42 Two- and three-phase power can be extended to N-phase power. In
such a scheme, the N-110-V/60-Hz signals are given by:

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