Using Complex Variables In Symbolic Calculations; Complex Numbers And Degree Mode - Texas Instruments TITANIUM TI-89 User Manual

REAL
RECTANGULAR
POLAR

Using Complex Variables in Symbolic Calculations

Using Complex Variables in Symbolic Calculations
Using Complex Variables in Symbolic Calculations 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
character in the variable name to designate a complex variable. For example:
z_ is treated as a
complex variable if it
does not have a stored
value.
Store an unreal value into any variable. For example:
Method 2:
x+yi!z
Then z is treated as a
complex variable.
Note: For best results in calculations such as

Complex Numbers and Degree Mode

Complex Numbers and Degree Mode Complex Numbers and Degree Mode 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 i i i
generally true because the values for cos and sin are converted to radians, while those
for e^( ) are not. For example, e^( i i i i 45) = cos(45) + i i i i sin(45) is treated internally as e^( i i i i 45)
= cos( /4) + i i i i 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
Degree or Gradian angle mode, an
Appendix B: Technical Reference
Will not display complex results unless you:
• Enter a complex number.
– or –
• Use a complex function such as
, or
cSolve() cZeros()
If complex results are displayed, they will be
shown in either a+bi or r e
Note: You can enter complex numbers in any
form (or a mixture of all forms) depending on
the Angle mode.
Displays complex results as a+bi.
Displays complex results as:
i
•
q
r e if the Angle mode = Radian
– or –
•
ùq)
(r , Angle
if the
Gradian
i i i i entry causes an error.
q
r e
cFactor()
.
i
q form.
Degree or
mode =
and
cSolve() cZeros()
) = cos( ) + i sin(
q q
,
2
) as the last
, use Method 1.
) are not
q
. In
q)
(r
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