# Knowledge Base

## Solution 11868: Certain Polar Values Not Computed on the TI-89 Family, TI-92 Family, and Voyage™ 200 Graphing Calculators.

### Why do the TI-89 family, TI-92 family, and Voyage 200 graphing calculators not compute some polar values?

The TI-89 family, TI-92 Plus, and Voyage 200 will not always return computed results for complex polar values in EXACT or AUTO modes. These calculators internally compute expressions in rectangular form that are then converted into polar form. Converting a very complicated expression in rectangular form to polar form while the calculator is in EXACT or AUTO mode can be extraneous on the Computer Algebra System (CAS). Internal complex calculations are calculated in rectangular form. So, the polar complex numbers are converted to rectangular form, then the computation (a * b) / (a + b) is performed. Finally, the resulting rectangular complex number is converted to polar form. It is a difficult process and takes several minutes to compute.

Simple looking inputs may generate very large exact outputs and may take a great deal of time to compute. If fast times or small output is desired, it is sometimes best to interrupt a computation and approximate it.

Example: (250 < 85)*(121 < 3)/((250 < 85)+(121 < 3))

The exact solution to this is...

(30250*(62500*(cos(3))2*(cos(5))4+(125000*(sin(5))2*(cos(3))2+60500*sin(5)*cos(3)+14641)*(cos(5))2+60500*sin(3)*cos(5)+62500*(sin(5))4*(cos(3))2+60500*(sin(5))3*cos(3)+14641*(sin(5))2+62500*(sin(3))2)/(60500*sin(3)*cos(5)+60500*sin(5)*cos(3)+77141) (atan((121*cos(5)+250*sin(3)) (250*cos(3)*(cos(5))^2+sin(5)*(250*sin(5)*cos(3)+121))))

The TI-89 family calculator using operating system version 2.09 took 45 minutes to return this answer. The approximate answer (103.416 < 27.1821) is generated in about 1 second.

Please see the TI-89 family, TI-92 family and Voyage 200 guidebooks for additional information.