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Chapter 2: Q7P (page 59)
: Find the disk of convergence for each of the followingcomplex power series.
The required disk of convergence is .
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Express the following complex numbers in the x + iy 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.
17.
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.
20.
Describe geometrically the set of points in the complex plane satisfying the following equations. .
Find the absolute value of each of the following using the discussion above. Try to do simple problems like these in your head-it saves time.
.
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 .
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