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Chapter 2: Q5MP (page 80)
Find one or more values of each of the following complex expressions and compare with acomputer solution.
The value of is, i .
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Solve for all possible values of the real numbers and in the following equations.
For each of the following numbers, first visualize where it is in the complex plane. With a little practice, you can quickly find in your head for these simple problems. Then plot the number and label it in five ways as in Figure 3.3. Also, plot the complex conjugate of the number.
.
Show from the power series (8.1) that .
Find the power series for and for from the series for in the following way: Write the series for ; put . Show that ; take real and imaginary parts of the equation, and put .
Use Problems 27 and 28 to find the following absolute values. If you understand Problems 27 and 28 and equation (5.1), you should be able to do these in your head.
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