Texas Instruments TI-89 User Manual - Page 938

REAL RECTANGULAR POLAR 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+bi or re iq form. 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: • re iq if the Angle mode = Radian - or - • (r ,ùq) if the Angle mode = Degree or Gradian 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 2 ) as the last 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. Method 2: Store an unreal value into any variable. For example: x+yi!z Then z is treated as a complex variable. 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^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^( ) are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(π/4) + i sin(π/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 (r ∠ q). In Degree or Gradian angle mode, an reiq entry causes an error. Appendix B: Technical Reference 939