Chapter 2: Complex Numbers
Q2P
Show from the power series (8.1) that .
Q2P
Find the disk of convergence for each of the following complex power series.
Q2P
In each of the following problems, z represents the displacement of a particle from the origin. Find (as functions of t) its speed and the magnitude of its acceleration, and describe the motion.
Q30MP
Write the series for. Writein theform and so obtain (easily) the powers of (). Thus show, for example, that theseries has noterm, noterm, etc., and a similar result for theseries. Find (easily) a formula for the general term for each series.
Q30P
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.
Q30P
Find each of the following in the x+iy form and check your answers by computer.
Q30P
Show that the sum of the three cube roots of 8is zero.
Q30P
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.
.
Q31MP
Show that if a sequence of complex numbers tends to zero, then the sequence of absolute values tends to zero too, and vice versa. Hintmeans and
Q31P
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.
.