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8.1 Complex Numbers JMerrill, 2009

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A Little History Math is used to explain our universe. When a recurring phenomenon is seen and cant be explained by our present mathematics, new systems of mathematics are derived. In the real number system, we cant take the square root of negatives, therefore the complex number system was created. Complex numbers revolutionized computer graphics

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Definition of the Imaginary Unit, i

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Complex Numbers A complex number consists of a real and an imaginary term:

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Operations on Complex Numbers Add/subtract real to real, and imaginary to imaginary Example:(6 + 7i) + (3 - 2i) (6 + 3) + (7i - 2i) = 9 + 5i When subtracting, DONT FORGET to distribute the negative sign! Example: (3+2i) – (5 – i) (3 – 5) + (2i – (-i)) = -2 + 3i

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Operations on Complex Numbers

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Dividing/Simplifying In order to simplify complex numbers (they must always be in the form a + bi, you must multiply by the complex conjugate:

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You Do Simplify:

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Operations with Complex Numbers

Operations with Complex Numbers

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