document.write( "Question 921632: (1+i)^100 find its imaginary part?? \r
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Algebra.Com's Answer #559172 by Theo(13342) $\"\"$ $\"About$

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the imaginary part will be equal to 0.
\n" ); document.write( "the imaginary part disappears every 4th iteration.
\n" ); document.write( "on the 25th iteration, the exponent = 100
\n" ); document.write( "you can use a calculator to confirm.
\n" ); document.write( "one such online calculation can be found here:
\n" ); document.write( "http://www.alcula.com/calculators/scientific-calculator/
\n" ); document.write( "using that calculator, i got:
\n" ); document.write( "(1+i)^100 = -1125899906842624
\n" ); document.write( "you can verify that every 4th iteration will cause the imaginary part to disappear.
\n" ); document.write( "simply use the calculator to calculate:
\n" ); document.write( "(1+i)^96
\n" ); document.write( "(1+i)^97
\n" ); document.write( "(1+i)^98
\n" ); document.write( "(1+i)^99
\n" ); document.write( "(1+i)^100
\n" ); document.write( "you will see that the imaginary part will be gone for the 96th power and for the 100th power.
\n" ); document.write( "here's the picture of what i did using the calculator.
\n" ); document.write( "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.\r
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