document.write( "Question 17359: find the value of -
\n" ); document.write( "(i+3^.5)^100 + (i-3^.5))^100 + 2)^100 \n" ); document.write( "
Algebra.Com's Answer #10040 by kapilsinghi(68)\"\" \"About 
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(i+root3)^100 +(i-root3)^100 + 2^100=?\r
\n" ); document.write( "\n" ); document.write( "i^100 = -1^50 = 1
\n" ); document.write( "so (i+root3)^100 = 1(i+root3)^100
\n" ); document.write( " = (i^100)(i+root3)^100
\n" ); document.write( " = (i(i+root3))^100
\n" ); document.write( " = (-1 + iroot3)^100\r
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\n" ); document.write( "\n" ); document.write( "similarly
\n" ); document.write( " (i-root3)^100 = (-1 - iroot3)^100
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\n" ); document.write( "w is cuberoot of unity
\n" ); document.write( "w + w^2 + 1 = 0
\n" ); document.write( "w^3n = 1\r
\n" ); document.write( "\n" ); document.write( " w = (-1 - iroot3)/2
\n" ); document.write( "=> 2w = (-1 - iroot3)
\n" ); document.write( "
\n" ); document.write( " w^2 = (-1 + iroot3)/2
\n" ); document.write( " 2w^2 = (-1 + iroot3) \r
\n" ); document.write( "\n" ); document.write( "so (i+root3)^100 + (i-root3)^100 + 2^100
\n" ); document.write( " = (-1 + iroot3)^100 + (-1 + iroot3)^100 + 2^100
\n" ); document.write( " = (-1 + iroot3)^100 + (-1 + iroot3)^100 + 2^100
\n" ); document.write( " = (2w)^100 + (2w^2)^100 + 2^100
\n" ); document.write( " = (2^100)*(w^100) + (2^100)*(w^200) + 2^100
\n" ); document.write( " = (2^100)(w^100 + (w^200) + 1)
\n" ); document.write( " = (2^100)(w*w^99 + (w^2)*(w^198) + 1)
\n" ); document.write( " = (2^100)(w + w^2 + 1)
\n" ); document.write( " = (2^100)(0)
\n" ); document.write( " = 0
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\n" ); document.write( "kapilsinghi123@gmail.com \n" ); document.write( "
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