Question

Evaluate i^26

Answer 1

-1*4^(-13i)

Answer 2

The book is saying -1?

Answer 3

Maybe 1?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

its clock addition

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

Then i^5-i^6=1?

Answer 13

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

Answer 14

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

Answer 15

26/4 = 8. R2

i^2 = -1

Answer 16

Got it! Thanks for your help!

Answer 17

haha amistre your quotient is wrong

Answer 18

lol.... I had a quotient ?

Answer 19

26/4=6. R2

Answer 20

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

Answer 21

lol

Answer 22

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