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anonymous

  • 5 years ago

Evaluate i^26

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  1. anonymous
    • 5 years ago
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    -1*4^(-13i)

  2. anonymous
    • 5 years ago
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    The book is saying -1?

  3. anonymous
    • 5 years ago
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    Maybe 1?

  4. anonymous
    • 5 years ago
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    sorry i'm not good with imaginary numbers. i just plugged it in the calculator and that's what i got.

  5. anonymous
    • 5 years ago
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    Yeah I'm not either. That's why I am here. Thanks anyway!

  6. myininaya
    • 5 years ago
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    26/4=6+remaider 2 i^2=-1

  7. amistre64
    • 5 years ago
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    its clock addition

  8. myininaya
    • 5 years ago
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    divide by 4 i^[4*6+2]=1^6i^2=1*(-1)=-1

  9. shadowfiend
    • 5 years ago
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    The best way to do this is to think about `sections' of i. We know the following four things: \[\begin{align} i^2 &= \sqrt{-1}^2 = -1\\ i^3 &= i^2 \cdot i = -1 \cdot i = -i\\ i^4 &= i^2 \cdot i^2 = -1 \cdot -1 = 1 \end{align}\] From that, we can derive any power of i. That's what myininaya has done.

  10. shadowfiend
    • 5 years ago
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    I said 4 --> I meant the following 3 things :) The fourth is that i is just i.

  11. anonymous
    • 5 years ago
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    I was coming up with( i^4)^5 *i^6

  12. anonymous
    • 5 years ago
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    Then i^5-i^6=1?

  13. shadowfiend
    • 5 years ago
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    Well, that's close. Note that \(i^6\) is actually \(i^{4 + 2}\), so it's really \((i^4)^6 \cdot i^2\).

  14. amistre64
    • 5 years ago
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  15. shadowfiend
    • 5 years ago
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    And since i^4 is always 1, 1^6 is always 1, you are left only with \(i^2\), which is -1.

  16. amistre64
    • 5 years ago
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    26/4 = 8. R2 i^2 = -1

  17. anonymous
    • 5 years ago
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    Got it! Thanks for your help!

  18. myininaya
    • 5 years ago
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    haha amistre your quotient is wrong

  19. amistre64
    • 5 years ago
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    lol.... I had a quotient ?

  20. myininaya
    • 5 years ago
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    26/4=6. R2

  21. amistre64
    • 5 years ago
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    LOL... yeah it is. but its so hard to remember all this stuff from kindergarten ;)

  22. myininaya
    • 5 years ago
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    lol

  23. anonymous
    • 5 years ago
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    Ouch you guys are killing me. This is actually Int Algebra - College.

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