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Chapter 2: Q19P (page 74)
Evaluate each of the following in x+ iyform, and compare with a computer solution.
The value of is .
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Describe geometrically the set of points in the complex plane satisfying the following equations.
.
Test each of the following series for convergence.
Express the following complex numbers in the form. Try to visualize each complex number, using sketches as in the examples if necessary. The first twelve problems you should be able to do in your head (and maybe some of the others—try it!) Doing a problem quickly in your head saves time over using a computer. Remember that the point in doing problems like this is to gain skill in manipulating complex expressions, so a good study method is to do the problems by hand and use a computer to check your answers.
4.
Follow steps (a), (b), (c) above to find all the values of the indicated roots .
For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly findin 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.
role="math" localid="1658473180216" .
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