Algebra.Com's Answer #662388 by ikleyn(52914)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "z^2=5-12i
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document.write( "Where z=a+bi
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document.write( "How to do it, help ls
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document.write( "z = a + bi --->  =  =  =  (since  =  =  =  // <--- since  = -1)\r\n" );
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document.write( "Now you have, from the condition, an equality of these two complex numbers:\r\n" );
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document.write( " = 5 - 12i.\r\n" );
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document.write( "It means that the real parts are equal and the imaginary parts are equal:\r\n" );
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document.write( " = 5, (1)\r\n" );
document.write( "2ab = -12. (2)\r\n" );
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document.write( "It is the system of two equations for the two unknowns \"a\" and \"b\".\r\n" );
document.write( "To solve it, express b =  =  from (2) and substitute it into (1). You will get\r\n" );
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document.write( " = 5, or\r\n" );
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document.write( " -  = 5.\r\n" );
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document.write( "Multiply both sides by a^2. You will get\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Factor the left side\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "The equation deploys in two independent equations\r\n" );
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document.write( "1.  = 0 ---> = 9 ---> a = +/- 3 ---> b = -6/a = -/+ 2.\r\n" );
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document.write( "2.  = 0 ---> = -4 ---> No real solutions.\r\n" );
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document.write( "Answer. The solutions of the original equation = 5 - 12i are these two complex numbers:  = 3 - 2i or/and  = -3 + 2i.\r\n" );
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document.write( " In other words, the square root of the complex number 5 - 12i in the complex domain are these two complex numbers: 3 - 2i and -3 + 2i.\r\n" );
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document.write( "There is a bunch of my lessons on complex numbers\r
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document.write( " - Complex numbers and arithmetical operations on them\r
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document.write( " - Complex plane\r
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document.write( " - Addition and subtraction of complex numbers in complex plane\r
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document.write( " - Multiplication and division of complex numbers in complex plane\r
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document.write( " - Raising a complex number to an integer power\r
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document.write( " - How to take a root of a complex number\r
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document.write( " - Solution of the quadratic equation with real coefficients on complex domain\r
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document.write( " - How to take a square root of a complex number\r
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document.write( " - Solution of the quadratic equation with complex coefficients on complex domain\r
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document.write( "in this site.\r
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