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8.1 Complex Numbers

8.1 Complex Numbers. JMerrill, 2009. A Little History . Math is used to explain our universe. When a recurring phenomenon is seen and can’t be explained by our present mathematics, new systems of mathematics are derived.

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8.1 Complex Numbers

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  1. 8.1Complex Numbers JMerrill, 2009

  2. A Little History  • Math is used to explain our universe. When a recurring phenomenon is seen and can’t be explained by our present mathematics, new systems of mathematics are derived. • In the real number system, we can’t take the square root of negatives, therefore the complex number system was created. • Complex numbers revolutionized computer graphics

  3. Definition of the Imaginary Unit, i

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

  5. 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, DON’T FORGET to distribute the negative sign! • Example: (3+2i) – (5 – i) • (3 – 5) + (2i – (-i)) = -2 + 3i

  6. Operations on Complex Numbers

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

  8. You Do • Simplify:

  9. Calculator 

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