## Friday, March 30, 2018

### Scientific Calculators Two Ways of Entering Complex Numbers

Scientific Calculators Two Ways of Entering Complex Numbers

On scientific calculators, there are two primary ways complex numbers are entered:

1. Using the [ a ] and [ b ] keys

2. Using a + bi notation

Complex Numbers using the [ a ] and [ b ] Keys

Calculators:  Canon F-605, Sharp EL-501X, Texas Instruments TI-35 Plus, Texas Instruments TI-52, most bargain Dollar Store calculators

This applies to most basic level scientific calculators.  Only arithmetic operations and polar/rectangular conversions apply in this mode.

Entering complex numbers:   real part [ a ] imaginary part [ b ]

Entering polar complex numbers (for conversion to rectangular complex numbers only):  magnitude [ a ] argument/angle [ b ]

Please be aware that in this mode where the [ a ] and [ b ] keys have to be used, the order of operations are not followed.

Example:  (3 + 3i) + (2 + 3i) * (4 + 3i)
(What is really calculated:  ((3 + 3i) + (2 + 3i)) * (4 + 3i))

Key Strokes: (in complex mode)
3 [ a ] 3 [ b ] [ + ] 2 [ a ] 3 [ b ] [ × ] 4 [ a ] 3 [ b ] [ = ]

Result:  2 + 39i (2 is stored in a, 39 is stored in b)

Example:  Transform 8 – 3i to Polar representation, use degrees mode

Key Strokes: (in complex mode)
Press [ DRG ] until the calculator is in Degrees mode (DEG indicator)
8 [ a ] 3 [ +/- ] [ b ] [ 2nd/SHIFT/INV ] (RP, rθ)

Result:
([ a ]) 8.544003745  ( r )
[ b ] -20.55604522 ( θ )

Complex Numbers using the a + bi Notation

Calculators:  most multi-line scientific calculators (Casio fx-115ES, fx-991ES, fx-991 Classwiz, Texas Instruments TI-36X Pro, Sharp EL-W516, Canon F-792SGA, most graphing calculators

Complex numbers using a + bi notation are entered exactly as they are written.  This mode is present on more advanced scientific calculators, particular the multiline calculators, as well as all graphing calculators.   The ability to calculate and display complex numbers may be turned on in a separate mode, or turned on through a set up menu.

Typically the available functions for complex numbers are:

* Arithmetic
* Inverse
* Square
* Polar/Rectangular Conversion
* Absolute Value
* Argument
* Real and Imaginary Parts
* Conjugate
* Square Roots (graphing calculators, all HP calculators with complex numbers)
* Exponentials and Logarithms (graphing calculators, all HP calculators with complex numbers)
* Powers, both real and complex (graphing calculators, all HP calculators with complex numbers)
* Trigonometric functions (TI-85, TI-86, TI-89, Casio Classpad, all HP calculators with  complex numbers)

In this complex numbers mode, the order of operations is followed.

Example:  (3 + 3i) + (2 + 3i) * (4 + 3i)

Key Strokes:  (*key strokes may vary)
[ ( ] 3 [ + ] 3 [ i ] [ ) ] [ + ] [ ( ] 2 [ + ] 3 [ i ] [ ) ] [ × ] [ ( ] 4 [ + ] 3 [ i ] [ ) ]

Result:  2 + 21i (2 [ Re<>Im ] 21)

Example:  Transform 8 – 3i to Polar representation, use degrees mode

Key Strokes: (in complex mode)
Press [ DRG ] until the calculator is in Degrees mode (DEG indicator)

Alternative 1:  (8 – 3i) >rθ,  (8 – 3i)>Polar

Alternative 2:
r:  abs(8 – 3i)
θ: angle(8 – 3i), arg(8 – 3i)

Result:
8.54003745 -20.5604522,  8.54003745*e^(-20.5604522*i)

That is two primary ways how complex numbers are entered on scientific calculators.

Eddie

All original content copyright, © 2011-2018.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.  Please contact the author if you have questions.

#### 1 comment:

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