anonymous
  • anonymous
Evaluate i^26
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
-1*4^(-13i)
anonymous
  • anonymous
The book is saying -1?
anonymous
  • anonymous
Maybe 1?

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anonymous
  • anonymous
sorry i'm not good with imaginary numbers. i just plugged it in the calculator and that's what i got.
anonymous
  • anonymous
Yeah I'm not either. That's why I am here. Thanks anyway!
myininaya
  • myininaya
26/4=6+remaider 2 i^2=-1
amistre64
  • amistre64
its clock addition
myininaya
  • myininaya
divide by 4 i^[4*6+2]=1^6i^2=1*(-1)=-1
shadowfiend
  • shadowfiend
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.
shadowfiend
  • shadowfiend
I said 4 --> I meant the following 3 things :) The fourth is that i is just i.
anonymous
  • anonymous
I was coming up with( i^4)^5 *i^6
anonymous
  • anonymous
Then i^5-i^6=1?
shadowfiend
  • shadowfiend
Well, that's close. Note that \(i^6\) is actually \(i^{4 + 2}\), so it's really \((i^4)^6 \cdot i^2\).
amistre64
  • amistre64
1 Attachment
shadowfiend
  • shadowfiend
And since i^4 is always 1, 1^6 is always 1, you are left only with \(i^2\), which is -1.
amistre64
  • amistre64
26/4 = 8. R2 i^2 = -1
anonymous
  • anonymous
Got it! Thanks for your help!
myininaya
  • myininaya
haha amistre your quotient is wrong
amistre64
  • amistre64
lol.... I had a quotient ?
myininaya
  • myininaya
26/4=6. R2
amistre64
  • amistre64
LOL... yeah it is. but its so hard to remember all this stuff from kindergarten ;)
myininaya
  • myininaya
lol
anonymous
  • anonymous
Ouch you guys are killing me. This is actually Int Algebra - College.

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