document.write( "Question 1123522: deduce the solutions of the equation
\n" ); document.write( "(z + 1)˄4 = 16(z - 1)˄4. \n" ); document.write( "
Algebra.Com's Answer #740205 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Here's a better approach:\r\n" );
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document.write( "\"%28z+%2B+1%29%5E4+=+16%28z+-+1%29%5E4\"\r\n" );
document.write( "Use the principle of square roots:\r\n" );
document.write( "\"sqrt%28%28z+%2B+1%29%5E4%29+=+%22%22+%2B-+sqrt%2816%28z+-+1%29%5E4%29\"\r\n" );
document.write( "\"%28z+%2B+1%29%5E2+=+%22%22+%2B-+4%28z+-+1%29%5E2\"\r\n" );
document.write( "Break that into two equations\r\n" );
document.write( "\"%28z+%2B+1%29%5E2+=+4%28z+-+1%29%5E2\"; \"%28z+%2B+1%29%5E2+=+-4%28z+-+1%29%5E2\"\r\n" );
document.write( "Use the principle of square roots again:\r\n" );
document.write( "\"sqrt%28%28z+%2B+1%29%5E2%29+=+%22%22+%2B-+sqrt%284%28z+-+1%29%5E2%29\"; \"sqrt%28%28z+%2B+1%29%5E2%29+=+%22%22+%2B-+sqrt%28-4%28z+-+1%29%5E2%29\"\r\n" );
document.write( "\"z+%2B+1+=+%22%22+%2B-+2%28z+-+1%29%29\"; \"z+%2B+1+=+%22%22+%2B-+2i%28z+-+1%29%29\"\r\n" );
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document.write( "We solve the first using the + :\r\n" );
document.write( "\"z+%2B+1+=+2%28z+-+1%29%29\";\r\n" );
document.write( "\"z+%2B+1+=+2z+-+2%29\"\r\n" );
document.write( "\"-z+=+-+3%29%29\"\r\n" );
document.write( "\"z=3\"\r\n" );
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document.write( "We solve the first using the - :\r\n" );
document.write( "\"z+%2B+1+=+-2%28z+-+1%29%29\";\r\n" );
document.write( "\"z+%2B+1+=+-2z+%2B+2\"\r\n" );
document.write( "\"3z+=1%29%29\"\r\n" );
document.write( "\"z=1%2F3\"\r\n" );
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document.write( "We solve the second using the + :\r\n" );
document.write( "\"z+%2B+1+=+2i%28z+-+1%29%29\";\r\n" );
document.write( "\"z+%2B+1+=+2iz+-+2i\"\r\n" );
document.write( "\"z-2iz+=-1-2i\"\r\n" );
document.write( "\"z%281-2i%29=-1-2i\"\r\n" );
document.write( "\"z=%28-1-2i%29%2F%281-2i%29\"\r\n" );
document.write( "\"z=%28-1-2i%29%2F%281-2i%29\"\"%22%22%2A%22%22\"\"%281%2B2i%29%2F%281%2B2i%29\"\r\n" );
document.write( "\"z=%28-1-2i-2i-4i%5E2%29%2F%281-4i%5E2%29\"\r\n" );
document.write( "\"z=%28-1-4i-4%28-1%29%29%2F%281-4%28-1%29%29\"\r\n" );
document.write( "\"z=%28-1-4i%2B4%29%2F%281%2B4%29\"\r\n" );
document.write( "\"z=%283-4i%29%2F5\"\r\n" );
document.write( "\"z=3%2F5-expr%284%2F5%29i\"\r\n" );
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document.write( "We could solve the second using the - the same way,\r\n" );
document.write( "but since we know that if a polynomial equation with real\r\n" );
document.write( "rational coefficients has a certain complex imaginary \r\n" );
document.write( "solution, then its conjugate is also a solution.\r\n" );
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document.write( "So \"z=3%2F5%2Bexpr%284%2F5%29i\" is also a solution.\r\n" );
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document.write( "The four solutions are:\r\n" );
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document.write( "\"3\", \"1%2F3\", \"3%2F5%2Bexpr%284%2F5%29i\", and \"3%2F5-expr%284%2F5%29i\"\r\n" );
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document.write( "Edwin
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