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Algebra Level 2

$\Huge i^{234} = \ ?$

i -1 1 Cannot be determined 0 -i

11 solutions

Abdullah Qureshi
Jun 23, 2015

Typo, first term is $i^{234}$ not $i^{243}$ .

Vishnu Bhagyanath - 5 years, 11 months ago

Thanks man, I have edited my solution.

Abdullah Qureshi - 5 years, 11 months ago

Brendan Warner
Jun 22, 2015

Observe that
$i^2 = -1$ ,
$i^3 = -i$ ,
$i^4 = 1$ ,
$i^5 = i$ ,

And this pattern repeats every four numbers, to find the answer, we must find out where the pattern stops in the case of i^234. So we divide 234/how often the pattern repeats. The remainder of 234/4 = 2 , and i^2 = -1

Then, $i^{234} = -1$ .

Moderator note:

Simple standard approach :)

FYI To type in Latex, all that you have to do is use the brackets $\backslash( \quad \backslash)$ around your equations, and check that that appear as you wish.

I've edited your solution slightly, so you can take a look at it and see how it works.

Calvin Lin Staff - 5 years, 11 months ago

Neil Ryan Manolong
Jul 7, 2015

I^234 is divisible by 2 which is equal to i^2 which is also equal to -1

Arulyan Asokan
Jul 5, 2015

Divide the power of "i" by 4, if the remainder is zero, the value of, "i" is 1. If the remainder is 1 then the value of, "i" is i. If the remainder is 2, then the value of, "i" is -1. If the remainder is 3, then the value of, "i" is -i.