Solution 12005: Unexpected Complex Answer Results (i Imaginary) on the TI-83 Family, TI-84 Plus Family and TI-Nspire™ Handheld in TI-84 Plus Mode.
Why does the TI-83 family, TI-84 Plus family and TI-Nspire handheld in TI-84 Plus mode not return -i when calculating i^7?
The answer displayed when calculating i^7 is the complex number -3E-13-i. The real part, -3E-13, is an approximation of zero. Thus, -3E-13-i is the same as 0-i which is equal to -i. With certain computations, these calculators use very sophisticated algorithms to calculate the most accurate answer possible. The same algorithm will also approximate for zero for other examples such as i^8 or i^9.
Some calculators use rounding schemes to generate expected answers within a certain tolerance. However, this has the potential to create problems in some types of calculations. Therefore, Texas Instruments decided to use no rounding schemes on the TI-83 family or TI-84 Plus family graphing calculator.
Please see the TI-83 family and TI-84 Plus family guidebooks for additional information.
NOTE: TI-Nspire users in TI-84 Plus mode may reference the TI-84 Plus family guidebook.