document.write( "Question 1123522: deduce the solutions of the equation
\n" ); document.write( "(z + 1)˄4 = 16(z - 1)˄4.
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Algebra.Com's Answer #739873 by Alan3354(69443)\"\" \"About 
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(z + 1)^4 = 16(z - 1)^4
\n" ); document.write( "(z + 1)^4 = 2^4*(z - 1)^4
\n" ); document.write( "(z + 1)^4 = (2z - 2)^4
\n" ); document.write( "z+1 = 2z-2
\n" ); document.write( "z = 3
\n" ); document.write( "=================
\n" ); document.write( "\"z%5E4+%2B+4z%5E3+%2B+6z%5E2+%2B+4z+%2B+1+=+16z%5E4+-+64z%5E3+%2B+96z%5E2+-+64z+%2B+16\"
\n" ); document.write( "\"15z%5E4+-+68z%5E3+%2B+90z%5E2+-+68z+%2B+15+=+0\"
\n" ); document.write( "Divide by (z-3)
\n" ); document.write( "---
\n" ); document.write( "\"15z%5E3+-+23z%5E2+%2B+21z+-+5+=+0\"
\n" ); document.write( "By graphical methods (or by Newton's method) z = 1/3
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\n" ); document.write( "Divide by (z-1/3)
\n" ); document.write( "\"15z%5E2+-+18z+%2B+15+=+0\"
\n" ); document.write( "\"5z%5E2+-+6z+%2B+5+=+0\"
\n" ); document.write( "---
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"5x%5E2%2B-6x%2B5+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-6%29%5E2-4%2A5%2A5=-64\".
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\n" ); document.write( " The discriminant -64 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -64 is + or - \"sqrt%28+64%29+=+8\".
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\n" ); document.write( " The solution is \"x%5B12%5D+=+%28--6%2B-i%2Asqrt%28+-64+%29%29%2F2%5C5+=++%28--6%2B-i%2A8%29%2F2%5C5+\", or
\n" ); document.write( " Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-6%2Ax%2B5+%29\"

\n" ); document.write( "\n" ); document.write( "z = (3/5) + 4i/5
\n" ); document.write( "z = (3/5) - 4i/5\r
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