EC-4044 (650-0808) Complex Entries Faxback Doc. # 3574
The EC-4044 is designed to recognize a rectangular or polar complex
number. The punctuation joining the two parts is a signal for the
calculator to handle the entry as a complex number. You can use a complex
number at the same places in an expression where you might use a real
number.
Parts of a The two perpendicular directions of the complex plane
Complex Number are real and imaginary. A point in the complex plane
is described by a coordinate pair that states its
distance from the origin in the real and imaginary
directions.
(real, imaginary)
These are the rectangular coordinates. The same point
also has a coordinate pair that states the magnitude
and direction measured as an angle from the positive
real direction.
These are the polar coordinates. The calculator
recognizes both forms of complex number entries and has
settings for complex results to appear in either polar
or rectangular form.
Instead of a coordinate pair, rectangular complex
numbers are often written as a vector with a pair of
terms:
a+ bi in nonelectrical applications or
a+ bj in electrical applications,
where i or j represents the square root of -1. The "a"
term is the real direction and the "b" term is the
imaginary direction. The terms of the vector directly
correspond to the rectangular coordinates.
Entering a The syntax for a complex number in rectangular form is:
Complex Number
In Rectangular (real, imaginary)
Form
1. Begin with an open parenthesis.
2. Follow it with the real part.
3. Type a comma (,).
4. After the comma, include the imaginary part.
5. End the entry with a close parenthesis.
Entering a The syntax for a complex number in polar form is:
Complex Number
in Polar Form 1. Begin with an open parenthesis.
2. Follow it with the magnitude.
3. Type the angle separator (2nd [<]).
4. After the angle separator, include the angle.
5. End the entry with a close parenthesis.
Be sure that the angle units setting matches the
angle you are entering for the angle part of the
number.
Viewing a The calculator has a setting for the form of a complex
Complex Number result. The two choices for this setting are
rectangular or polar.
-> If the rectangular form for complex results is
selected, the display shows the RE indicator.
-> If the polar form for complex results is selected,
the display shows the PO indicator.
To change this setting, press 3rd [RP>]. This setting
affects only the way answers are displayed. Therefore,
it does not limit your choice of entering a complex
number in either polar or rectangular form.
Note: A polar complex number is handled internally in
rectangular form. The calculator makes two conversions
(first to rectangular and then back to polar) when
polar results are selected. Also, the mathematics
reduce the number to certain circular equivalents for
rotational multiples or a negative magnitude.
Consequently, a polar result is equivalent to, but many
have a different appearance than, the expected result.
You can avoid most rounding discrepancies by setting
the calculator for 10 digits (a selection of 2nd
[13>]).
The two parts of a complex number often will cause it
to be longer than the visible display. You can use the
<- and -> keys to scroll the display to view the entire
complex number.
The parts of a complex number are shown according to
the calculator's notation setting. If you select
scientific or engineering notation, or if you select a
fixed decimal point, both parts of a result appear in
that notation.
Restrictions on If you attempt to use a complex number with the
Complex Entries following functions, an error condition occurs.
Angle conversions Integration
Base conversions Logical operators
Combinations Metric conversions
Deg/min/sec conversions Percent
Delta percent Permutations
Factorial Polynomial root finding
Fractional portion Signum
Integer portion Statistics
A complex number must be in the decimal number base.
Angle You can convert the angle of a polar complex number
Consideration from one angle unit to another. Include the
appropriate angle conversion following the angle of the
complex number, such as:
(4<30D>R)
It is also appropriate for you to change the angle
units setting to match the result of the conversion.
The result is the same complex number, but it has new
angle units.
Although you can place an angle conversion function
with part of a complex number, using an angle
conversion with an entire complex number causes an
error. Attempting to convert a rectangular number to
rectangular form or a polar number to polar form also
causes an error condition.
You should select radians when using trigonometric
functions with complex numbers. Otherwise, the units
indicated in the display do not match the calculated
values. If you select degrees or grads, complex
trigonometric functions calculate a point in the
complex plane as if radians were selected. However, if
the polar form of complex numbers is selected, the
angle of a result is displayed in the currently
selected angle units.
Using Complex Numbers in Functions
You perform calculations with complex numbers in a
natural straightforward sequence. Many functions are
defined with a complex range outside of the real range.
This enables the calculator to give you an answer
instead of an error condition that you would encounter
with most other calculators.
Results of When you calculate a function of a real number:
Functions
-> If the answer is a real number, a single value
results.
-> If the answer is complex, a pair of values in the
form of a complex number results.
When you calculate a function of a complex number, the
result is a complex number (except for absolute value,
first coordinate, or second coordinate, which yield a
real result). When the answer has an imaginary part
that is zero, the imaginary part remains with the
number.
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