document.write( "Question 1209643: Find all complex solutions to the equation z^4 = -64 - 16z^2.\r
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\n" ); document.write( "\n" ); document.write( "Enter all the solutions in the form $a + bi$, where $a$ and $b$ are real numbers. \n" ); document.write( "
Algebra.Com's Answer #849719 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Find all complex solutions to the equation z^4 = -64 - 16z^2.\r
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document.write( "An equation\r\n" );
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document.write( "    z^4 = -64 - 16z^2\r\n" );
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document.write( "is equivalent to\r\n" );
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document.write( "    z^4 + 16z^2 + 64 = 0,\r\n" );
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document.write( "    \"%28z%5E2+%2B+8%29%5E2\" = 0.\r\n" );
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document.write( "Over complex numbers, the last equation can be factored\r\n" );
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document.write( "    \"%28%28z+%2B+2i%2Asqrt%282%29%29%2A%28z+-+2i%2Asqrt%282%29%29%29%5E2\" = 0,\r\n" );
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document.write( "or\r\n" );
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document.write( "    \"%28z%2B2i%2Asqrt%282%29%29%5E2%2A%28z-2i%2Asqrt%282%29%29%5E2\" = 0.\r\n" );
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document.write( "It means that the given equation has these 4 roots\r\n" );
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document.write( "    z = \"-2i%2Asqrt%282%29\"  of the multiplicity 2,  and  z = \"2i%2Asqrt%282%29\"  of the multiplicity 2.    ANSWER\r\n" );
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