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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ComplexReview - Math 254 Review information on arithmetic...

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