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. (br/all-12/12/94)