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

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Unformatted text preview: Lecture 15: Section 2.4 Complex Numbers Consider the equation u1D465 2 = − 1. Def. The imaginary unit , u1D456 , is the number such that u1D456 2 = − 1 or u1D456 = √ − 1 Power of u1D456 u1D456 1 = √ − 1 = u1D456 u1D456 2 = − 1 u1D456 3 = u1D456 4 = u1D456 5 = u1D456 6 = u1D456 7 = u1D456 8 = Therefore, every integer power of u1D456 can be written as u1D456, − 1 , − u1D456, 1. In general, divide the exponent by 4 and rewrite: ex. 1) u1D456 85 2) ( − u1D456 ) 85 3) u1D456 100 4) ( − u1D456 ) − 18 Def. Complex numbers are numbers of the form u1D44E + u1D44Fu1D456 , where u1D44E and u1D44F are real numbers. u1D44E is the real part and u1D44F is the imaginary part of the complex number u1D44E + u1D44Fu1D456 . u1D44E + u1D44Fu1D456 is called the standard form of a complex number. ex. Write the number − 5 as a complex number. NOTE: The set of real numbers is a subset of the set of complex numbers....
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This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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

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