document.write( "Question 464918: (1+i) to the 100th. I have a TI-89 that will solve this and the answer is -1.1259E15 but how was the solution derived? \n" ); document.write( "

Algebra.Com's Answer #318490 by richard1234(7193) $\"\"$ $\"About$

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If we were to expand the whole thing,\r
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\n" ); document.write( "\n" ); document.write( "We see that the real part is\r
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\r
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\n" ); document.write( "\n" ); document.write( "and the imaginary part is\r
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\r
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\n" ); document.write( "\n" ); document.write( "All of the imaginary terms cancel out, because we can group the terms together, noting that nCk = nC(n-k):\r
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\n" ); document.write( "\n" ); document.write( "Hence, we are left with the real part, which happens to be that real number you posted. \n" ); document.write( "

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