Question

If i is raised to an even power, then it can not simplify to be
-1
1
i

Answer 1

do you know the definition of
'i'
?

Answer 2

find
i^2
i^4
i^6
i^8
...
see the pattern,
you'll get your answer :)

Answer 3

yes its the imaginary quantity equal to the square root of minus one.

Answer 4

I know the definition, not how to do it.

Answer 5

so
\(i = \sqrt{-1}\)

square it,
what do u get ?

Answer 6

I don't understand the entire content of "imaginary numbers" it doesn't click with me. How can I answer it if i don't understand it?

Answer 7

you understand squaring ?

and \((\sqrt{a})^2 =a\)
thats basic exponent rule.

if you're not comfortable with "imaginary" term,
assume 'i' as a variable, like x

Answer 8

I have tried everything to learn imaginary numbers. teachers, tutors, anything to help my pass. I don't have a calculator so squaring by hand is a pain. let alone imaginary numbers. My brain just doesn't want to understand it. it makes no sense what so ever.

Answer 9

if \(x = \sqrt a\)
so, \(x^2 =a\)

do u understand that ?
nothing to do with imaginary numbers...

Answer 10

kind of.

Answer 11

ok, then try to answer this :
if \(i = \sqrt{-1} \\ then, \: i^2 = .. ?\)

Answer 12

1?

Answer 13

why 1? and why not -1 ?

where did the negative go ?
did you eat it ? :P

Answer 14

could have swore i put -1. I'm on a crap cromebook thinkpad thing, spacebar halfway works.

Answer 15

yes, I got hungry so i ate the negative.

Answer 16

cool, so,
\(i^2 =-1\)
is correct :)
now square both sides again,
what do u get ?

Answer 17

1

Answer 18

I think

Answer 19

correct again! :)

Answer 20

so,
i^2 =-1
i^4 = 1

so which value you cannot get ?
out of 1,-1, i
?

Answer 21

i

Answer 22

thats your answer :)

Answer 23

please refer to this also,
maybe you'll start understanding things :)
http://www.mathsisfun.com/numbers/imaginary-numbers.html

Answer 24

feel free to ask any doubts :)

Answer 25

thank you!

Answer 26

welcome ^_^