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mac1105_lecture7_1

# mac1105_lecture7_1 - L7 Complex Numbers and Quadratic...

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61 L7 Complex Numbers and Quadratic Equations Complex Numbers The imaginary unit , which we denote by i , is a solution of the equation 2 1 x = − , that is, 2 1 i =− . Another solution of this equation is ( i ). Complex numbers are the numbers of the form ab i + , where a and b are real. The real numbers a and b are called respectively the real part and imaginary part of the complex number i + . The form ai b + is the standard form of a complex number. A real number a can be written as 0 + , thus, the set of real numbers is a subset in the complex number system. Complex number bi is called a pure imaginary number . Equality of Complex Numbers : b ci d += + if and only if

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62 Sum of Complex Numbers : () ai b ci d ++ + = Product of Complex Numbers : b d = Note: The product of complex numbers is easy to find by using FOIL and the fact that 2 1 i =− . Complex Conjugates : The complex conjugate of a number za b i = + is b i . Example : Write expressions in the standard form.
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mac1105_lecture7_1 - L7 Complex Numbers and Quadratic...

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