You can put this solution on YOUR website! the imaginary part will be equal to 0.
the imaginary part disappears every 4th iteration.
on the 25th iteration, the exponent = 100
you can use a calculator to confirm.
one such online calculation can be found here: http://www.alcula.com/calculators/scientific-calculator/
using that calculator, i got:
(1+i)^100 = -1125899906842624
you can verify that every 4th iteration will cause the imaginary part to disappear.
simply use the calculator to calculate:
(1+i)^96
(1+i)^97
(1+i)^98
(1+i)^99
(1+i)^100
you will see that the imaginary part will be gone for the 96th power and for the 100th power.
here's the picture of what i did using the calculator.
look close for the i because it blends in. the i will be present for outputs 1, 2, and 3. the i will not be present for outputs 0, 4.
