Using complex variables in symbolic calculations, Complex numbers and degree mode – Texas Instruments TITANIUM TI-89 User Manual

Page 938

Appendix B: Technical Reference

939

Using Complex Variables in Symbolic Calculations

Regardless of the Complex Format mode setting, variables that have no stored value and those
that do not end with an underscore (_) are treated as real numbers. To perform complex symbolic
analysis, you can use either of the following methods to set up a complex variable.

Method 1:

Use an underscore _ (

TI-89 Titanium:

¥ 

Voyage™ 200



) as the last

character in the variable name to designate a complex variable. For example:

Method 2:

Store an unreal value into any variable. For example:

Note: For best results in calculations such as

cSolve()

and

cZeros()

, use Method 1.

Complex Numbers and Degree Mode

Radian angle mode is recommended for complex number calculations. Internally, the
TI-89 Titanium / Voyage™ 200 converts all entered trig values to radians, but it does not
convert values for exponential, logarithmic, or hyperbolic functions.

In Degree angle mode, complex identities such as e^(i

iii

) = cos(

) + i sin(

) are not

generally true because the values for cos and sin are converted to radians, while those
for e^( ) are not. For example, e^(i

iii45) = cos(45) + iiii sin(45) is treated internally as e^(iiii45)

= cos(

/4) + i

iii sin(

/4). Complex identities are always true in Radian angle mode.

Note: If you use Degree angle mode, you must make polar entries in the form

∠

)

. In

Degree or Gradian angle mode, an

iiii

entry causes an error.

REAL

Will not display complex results unless you:

•

Enter a complex number.

– or –

•

Use a complex function such as

cFactor()

cSolve()

, or

cZeros()

If complex results are displayed, they will be
shown in either a+b

or r

form.

Note: You can enter complex numbers in any
form (or a mixture of all forms) depending on
the Angle mode.

RECTANGULAR

Displays complex results as a+b

POLAR

Displays complex results as:

•

if the Angle mode = Radian

– or –

•

)

if the

Angle

mode =

Degree or

Gradian

z_ is treated as a
complex variable if it
does not have a stored
value.

x+y

Then z is treated as a
complex variable.