Question

radicals

Answer 1

@DanJS

Answer 2

i^6*i^8

Answer 3

this has to do with imaginary numbers. Still learning this concept.

Answer 4

ok,, not really too much to remember , this is the most important here...

Answer 5

\[i = \sqrt{-1} ~~~~~or~~~~~i^2 = -1\]

Answer 6

Start listing a chart for the powers of i....

Answer 7

i^1 =i
i^2 = -1
i^3 = i^2*i = -i
i^4 = i^2*i^2 = -1*-1 = 1

that is the cycle

Answer 8

i , -1 , -i, 1

then repeats

Answer 9

i^5 = i^4*i = i

Answer 10

Okay. So what about when it's 6 or 8? just double it?

Answer 11

the order for the first 4 powers is

i
-1
-i
1

For any other power, simply divide the power by 4, then the remainder is the number in the series above. For example
i^6

when divided by 4, remainder of 2, and the second spot in the series is -1

i^6 = -1

Answer 12

i^650

divide 650/4 first = 162+2/4 , the second term in the series above is -1, so

i^650 = -1d

Answer 13

i^650 = -1

Answer 14

divide the power by 4, then use the remainder as the spot in the series

i
-1
-i
1

Answer 15

Okay that makes more sense. So i^6 is -1 and i^8 would be divided by 4 right?

Answer 16

so

i^6 * i^8 = i^(6+8) = i^14

14/4 = 3 +2/4 , second one in the series is -1

i^6 * i^8 = i^14 = -1

Answer 17

if you cant remember the series, all you really have to know is i^2 = -1

i = i
i^2 = -1
i^3 = i^2*i = -1*i = -i
i^4 = i^2 * i^2 = -1*-1 = 1

Answer 18

Okay. so, i^6 * i^8 = -1? I should be able to remember it because I am allowed to take an 8 1/2 by 11 inch paper with me to the exam! didn't think my teacher would let us because I've never been able to do that before. I'll be sure to write that out on my paper.

Answer 19

*paper with notes on it with me

Answer 20

yeah, just write on it, i^2 = -1 and i = square root of -1

Answer 21

okay.

Answer 22

and the first 4 in the series

i
-1
-i
1

Answer 23

i^1054 = -1

Answer 24

1054/4 = 263 and 2/4

Answer 25

thanks!! : )