prcreva7

prcreva7 - conjugate is a nonnegative real number. Thus if...

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A.7 Complex Numbers; Quadratic Equations with a Negative Discriminant
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Complex numbers are numbers of the form a + bi , where a and b are real numbers. The real number a is called the real part of the number a + bi ; the real number b is called the imaginary part of a + bi .
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( a + bi ) + ( c + di ) = ( a + c ) + ( b + d ) i (2 + 4 i ) + (-1 + 6 i ) = (2 - 1) + (4 + 6) i = 1 + 10 i Sum of Complex Numbers
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( a + bi ) - ( c + di ) = ( a - c ) + ( b - d ) i (3 + i ) - (1 - 2 i ) = (3 - 1) + (1 - (-2)) i = 2 + 3 i Difference of Complex Numbers
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Product of Complex Numbers
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If z=a +bi is a complex number, then its conjugate, denoted by
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Theorem The product of a complex number and its
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Unformatted text preview: conjugate is a nonnegative real number. Thus if z=a +bi , then Theorem If N is a positive real number, we define the principal square root of -N as In the complex number system, the solution of the quadratic equation where a, b, and c are real numbers and are given by the formula Solve: Discriminant of a Quadratic Equation is called a discriminant >0, there are 2 unequal real solutions. =0, there is a repeated real solution. <0, there are two complex solutions. The solutions are conjugates of each other....
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This note was uploaded on 12/17/2010 for the course MATH 131 taught by Professor Staff during the Fall '08 term at UNC.

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prcreva7 - conjugate is a nonnegative real number. Thus if...

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