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Chapter 2: Q3P (page 59)
Find the disk of convergence for each of the following complex power series.
The entire complex plane is the region of convergence.
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Show from the power series (8.1) that .
Find each of the following in rectangular form if ; if .
For each of the following numbers, first visualize where it is in the complex plane. With a little practice you can quickly find x,y,r, 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.
-1.
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鈥攖ry 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.
14.
Find each of the following in rectangular form if ; if .
role="math" localid="1658486330935" .
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