Solution 12005: Unexpected Complex Answer Results (i Imaginary) on the TI-83 Plus, TI-84 Plus, and TI-84 Plus C Silver Edition.
Why does the TI-83 Plus, TI-84 Plus, and TI-84 Plus C Silver Edition 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 this type of calculation.
Please see the TI-83 Plus and TI-84 Plus Family guidebooks for additional information.
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