ComplexReview

# ComplexReview - Math 254 Review information on arithmetic...

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Math 254 Review information on arithmetic for complex numbers Complex numbers are deﬁned in terms of an “imaginary” number i which is a square root of - 1. Of course no real number could have a negative square, so i is a new kind of number. It turns out that using numbers of the form a + bi (complex numbers) where a and b are real numbers, you can ﬁnd roots for any polynomial, and in fact, any polynomial can be factored as a product of a constant and terms of the form x - r , where the r ’s are complex numbers. Complex numbers are very useful in diﬀerential equations, so it is worth reviewing some basic facts about them. To add or subtract two complex numbers, one simply adds (or subtracts) the corresponding real and imaginary parts. a + bi + c + di = ( a + c ) + ( b + d ) i, ( a + bi ) - ( c + di ) = ( a - c ) + ( b - d ) i. Multiplication is also straightforward ( a + bi )( c + di ) = ac + adi + bci + bdi 2 = ac + adi + bci - bd = ( ac - bd )+( ad + bc ) i. Division is a bit trickier.

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## This note was uploaded on 04/02/2008 for the course MATH 254 taught by Professor Indik during the Spring '08 term at Arizona.

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ComplexReview - Math 254 Review information on arithmetic...

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