1140 L15 - Lecture 15: Section 2.4 Complex Numbers Consider...

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Lecture 15: Section 2.4 Complex Numbers Consider the equation x 2 = ± 1. Def. The imaginary unit , i , is the number such that i 2 = ± 1 or i = p ± 1 Complex numbers are numbers of the form a + bi , where a and b are real numbers. a is the real part and bi is the imaginary part of the complex number a + bi . a + bi is the standard form of a complex number. NOTE: 1. If b = 0, the number a + bi = a + 0 i = a is a real number. Every real number can be written as a complex number by letting b = 0. The set of real numbers is a subset of the set of complex numbers. 2. If a = 0, the number 0 + bi = bi is called a pure imaginary number .
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Equality of Complex Numbers a + bi = c + di if and only if Operations with Complex Numbers Sum: ( a + bi ) + ( c + di ) = Di±erence: ( a + bi ) ± ( c + di ) = Multiplication: ( a + bi )( c + di ) = NOTE: Here, we use the distributive property (FOIL) and remember that i 2 = ± 1. ex. Write in standard form: 1) (1 + 2 i )(2 + 3 i ) = 2) 3(1 ± 5 i ) ± (2 ± 3 i )
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Complex Conjugates Def. The conjugate (complex conjugate) of a complex number z = a + bi is z = a + bi = ex.
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1140 L15 - Lecture 15: Section 2.4 Complex Numbers Consider...

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