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often frustrating if one lost minus sign or decimal point invalidates the
solution. Fortunately, technologists of today have calculators and computer
methods that make the process measurably easier with higher
degrees of reliability and accuracy.
Calculators
CALCULATOR AND COMPUTER METHODS WITH COMPLEX NUMBERS ⏐⏐⏐ 607
The TI-86 calculator of Fig. 14.58 is only one of numerous calculators
that can convert from one form to another and perform lengthy calculations
with complex numbers in a concise, neat form. Not all of the
details of using a specific calculator will be included here because each
has its own format and sequence of steps. However, the basic operations
with the TI-86 will be included primarily to demonstrate the ease with
which the conversions can be made and the format for more complex
operations.
For the TI-86 calculator, one must first call up the 2nd function
CPLX from the keyboard, which results in a menu at the bottom of the
display including conj, real, imag, abs, and angle. If we choose the key
MORE, � Rec and � Pol will appear as options (for the conversion
process). To convert from one form to another, simply enter the current
form in brackets with a comma between components for the rectangular
form and an angle symbol for the polar form. Follow this form with
the operation to be performed, and press the ENTER key—the result
will appear on the screen in the desired format.
EXAMPLE 14.27 This example is for demonstration purposes only. It
is not expected that all readers will have a TI-86 calculator. The sole
purpose of the example is to demonstrate the power of today’s calculators.
Using the TI-86 calculator, perform the following conversions:
a. 3 � j 4 to polar form.
b. 0.006 �20.6° to rectangular form.
Solutions:
a. The TI-86 display for part (a) is the following:
(3, �4) � Pol ENTER
(5.000E0��53.130E0)
CALC. 14.1
b. The TI-86 display for part (b) is the following:
(0.006�20.6) � Rec ENTER
(5.616E�3, 2.111E�3)
CALC. 14.2
EXAMPLE 14.28 Using the TI-86 calculator, perform the desired
operations required in part (c) of Example 14.26, and compare solutions.
Solution: One must now be aware of the hierarchy of mathematical
operations. In other words, in which sequence will the calculator perform
the desired operations? In most cases, the sequence is the same as
FIG. 14.58
TI-86 scientific calculator. (Courtesy of Texas
Instruments, Inc.)