document.write( "Question 1152858: i) Expand z = $\"%281%2Bic%29%5E6\"$ in powers of c
\n" ); document.write( "ii) Hence find the 5 real values of c for which z is real. \n" ); document.write( "

Algebra.Com's Answer #774970 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"%281%2Bic%29%5E6\"$

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\n" ); document.write( " $\"1+%2B+6ic+-+15c%5E2+-+20ic%5E3+%2B+15c%5E4+%2B+6ic%5E5+-+c%5E6\"$

\n" ); document.write( " $\"%281-15c%5E2%2B15c%5E4%29+%2B+%286c-20c%5E3%2B6c%5E5%29i\"$

\n" ); document.write( "We want the imaginary part to be 0:

\n" ); document.write( " $\"6c-20c%5E3%2B6c%5E5+=+0\"$
\n" ); document.write( " $\"2c%283-10c%5E2%2B3c%5E4%29+=+0\"$
\n" ); document.write( " $\"2c%283-c%5E2%29%281-3c%5E2%29+=+0\"$

\n" ); document.write( " $\"c=+0\"$ OR $\"c%5E2+=+3\"$ OR $\"c%5E2+=+1%2F3\"$

\n" ); document.write( "The 5 values of c for which the expression is real are
\n" ); document.write( " $\"0\"$
\n" ); document.write( " $\"sqrt%283%29\"$ and $\"-sqrt%283%29\"$
\n" ); document.write( " $\"sqrt%281%2F3%29\"$ and $\"-sqrt%281%2F3%29\"$
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