document.write( "Question 383150: Let z1, z2 and z3 be three complex numbers in geometric progression. Suppose that the
\n" ); document.write( "average of these numbers is 10, while the average of their squares is 20i. Determine the
\n" ); document.write( "value of z2, the middle term. \n" ); document.write( "
Algebra.Com's Answer #271379 by Jk22(389)\"\" \"About 
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Geometric progression means : z2=a*z1, z3=a^2*z1
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\n" ); document.write( " sum : \"z1%2A%28a%5E3-1%29%2F%28a-1%29=30\"
\n" ); document.write( " sum of square :
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\n" ); document.write( "the first sum squared is : \"z1%5E2%2A%28a%5E3-1%29%5E2%2F%28%28a-1%29%5E2%29=900\"
\n" ); document.write( " divided by the sum of squared :
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\n" ); document.write( "\"%28a%5E3-1%29%5E2%2F%28a-1%29%5E2%2A%28a%5E2-1%29%2F%28a%5E6-1%29=-20%2F3%2Ai\"\r
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\n" ); document.write( "\"%28a%5E3-1%29%2F%28a-1%29%2A%28a%2B1%29%2F%28a%5E3%2B1%29=-20%2F3%2Ai\"| use (a^3+1)=(a+1)(a^2-a+1)
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\n" ); document.write( "\"%28a%5E2-a%2B1%29%2F%28a%5E2%2Ba%2B1%29=-20%2F3%2Ai\"\r
\n" ); document.write( "\n" ); document.write( "\"a%5E2-a%2B1=-20%2F3%2Ai%2A%28a%5E2%2Ba%2B1%29\"\r
\n" ); document.write( "\n" ); document.write( "\"%281%2B20%2F3%2Ai%29a%5E2%2B%28-1%2B20%2F3%2Ai%29a%2B%281%2B20%2F3%2Ai%29=0\"
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\n" ); document.write( "Let \"D+=%28-1%2B20%2F3%2Ai%29%5E2-4%2A%281%2B20%2F3%2Ai%29%5E2\"
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\n" ); document.write( "then \"a=%28-%28-1%2B20%2F3%2Ai%29%2B-sqrt%28D%29%29%2F%282%281%2B20%2F3%2Ai%29%29\"\r
\n" ); document.write( "\n" ); document.write( "and \"z1=300%2F%28a%5E2%2Ba%2B1%29\" \n" ); document.write( "
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