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Mathematics 26 Online
OpenStudy (anonymous):

Evaluate i^26

OpenStudy (anonymous):

-1*4^(-13i)

OpenStudy (anonymous):

The book is saying -1?

OpenStudy (anonymous):

Maybe 1?

OpenStudy (anonymous):

sorry i'm not good with imaginary numbers. i just plugged it in the calculator and that's what i got.

OpenStudy (anonymous):

Yeah I'm not either. That's why I am here. Thanks anyway!

myininaya (myininaya):

26/4=6+remaider 2 i^2=-1

OpenStudy (amistre64):

its clock addition

myininaya (myininaya):

divide by 4 i^[4*6+2]=1^6i^2=1*(-1)=-1

OpenStudy (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.

OpenStudy (shadowfiend):

I said 4 --> I meant the following 3 things :) The fourth is that i is just i.

OpenStudy (anonymous):

I was coming up with( i^4)^5 *i^6

OpenStudy (anonymous):

Then i^5-i^6=1?

OpenStudy (shadowfiend):

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

OpenStudy (amistre64):

OpenStudy (shadowfiend):

And since i^4 is always 1, 1^6 is always 1, you are left only with \(i^2\), which is -1.

OpenStudy (amistre64):

26/4 = 8. R2 i^2 = -1

OpenStudy (anonymous):

Got it! Thanks for your help!

myininaya (myininaya):

haha amistre your quotient is wrong

OpenStudy (amistre64):

lol.... I had a quotient ?

myininaya (myininaya):

26/4=6. R2

OpenStudy (amistre64):

LOL... yeah it is. but its so hard to remember all this stuff from kindergarten ;)

myininaya (myininaya):

lol

OpenStudy (anonymous):

Ouch you guys are killing me. This is actually Int Algebra - College.

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