**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 ] (R→P, →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) >r∠θ, (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

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