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← i - College Algebra

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Showing Revision 2 created 05/25/2016 by Udacity Robot.

  1. Now since i is just another number, like all other numbers i to the 0 power is
  2. just equal to 1. This may seem a little bit funny, because 1 is a real number.
  3. But I think this is more a testament to the fact that i and all other imaginary
  4. numbers are in fact numbers, i to the first power is just i, i squared is i
  5. times itself. Which means we're multiplying the square root of negative 1 times
  6. the square root of negative 1, that should just give us negative 1. Now i cubed
  7. is going to be i squared times i. So we have negative 1 times i which is
  8. negative i. Interesting. So we only have ones and i's, the positive and negative
  9. versions over here. Let's see what happens in this column, i to the fourth
  10. should be i to the third times i again. That means we're multiplying the square
  11. root of negative 1 by itself and then taking the negative of that number. So
  12. this is negative, negative 1, which is just equal to 1. But that's funny, that's
  13. the same as i to the 0, i to the 5th is i to the 4th times i. So 1 times i which
  14. is i again. That's the same as i to the first. And we can see the pattern
  15. continues for i to the sixth and i to the seventh, so it seems like when we take
  16. powers of i, the numbers that they're equal to alternate in a cyclic way. We go
  17. from 1 to i to negative 1 to negative i back to 1 and so on. I think this
  18. pattern is really interesting, and keeping this in mind is going to help us
  19. remember the relationship between real numbers and imaginary numbers.