SOLUTION: (1+i)^100 find its imaginary part??

Question 921632: (1+i)^100 find its imaginary part??

Answer by Theo(13342) (Show Source): 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.

$$$

RELATED QUESTIONS
help! i dont understand this problem...i know what real and imaginary numbers are but... (answered by cartert,Mathtut,Fombitz)

Find the real part and imaginary part of... (answered by CharlesG2)

which are the real part and imaginary part of the complex number... (answered by ikleyn)

Find the real and imaginary parts of the complex number. 7 - (square root-11)... (answered by Alan3354)

5-3i/6+3i find the real and imaginary... (answered by palanisamy)

simplify: 7+2i(imaginary numer)+1-4i(imaginary number) (-4-8i(imaginary... (answered by MathLover1)

We use the Greek letter iota, i, to represent the square root of -1 ( ). We call i an... (answered by MathLover1)

how do i find all real or imaginary solutions?... (answered by Alan3354)

Question: If Following Are The Solutions Of 2 Quadratic Equations Equation 1: Real... (answered by sabanasir)