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← Complex Number Manipulation - College Algebra

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Showing Revision 2 created 05/24/2016 by Udacity Robot.

  1. Remember, that when we add and subtract complex numbers, the imaginary parts are
  2. like terms and the real parts are like terms. So we end up with 1 plus 3i plus
  3. the quanity negative 6 plus 2i equals negative 5 plus 5i. 1 plus 3i minus the
  4. quanity negative 6 plus 2i gives us 7 plus i. When we multiply complex numbers,
  5. this needs to happen by distributing in the same way that we did with binomials
  6. involving, involving variables. The quantity 1 plus 3i times the quantity
  7. negative 6 plus 2i, gives us negative 6, plus 2i, minus 18i, plus 6i squared.
  8. Which when simplified, gives us negative 6, minus 16i, minus 6 or negative 12
  9. minus 16i. And lastly, when we divided complex numbers, the final thing we need
  10. to do is to make the denominator into a real number, so that we can just let it
  11. modify the coefficients of the real and imaginary parts of the denominator. To
  12. change the denominator in this way, we multiply both the denominator and the
  13. numerator by the complex conjugate of the original denominator. So, negative 6
  14. minus 2i in this case. Now let's look at the problem. 1 plus 3i, divided by
  15. negative 6 plus 2i, gives us 1 plus 3i, times the conjugate negative 6 minus 2i,
  16. divided by negative 6 plus 2i, times negative 6 minus 2i. Simplifying further,
  17. we got negative 6 minus 2i minus 18i minus 6i squared, divided by 36 minus 4i
  18. squared. Which gives us negative six minus 20i plus 6, divided by 36 plus 4 or
  19. negative 20i over 40, and finally negative i over 2.