W versus iota

Algebra Level 2

$\displaystyle\omega^{x}=\iota^{x}$

What should replace $x$ in the above equation?

Note:Here $\omega$ is cube root of unity and $\iota=\sqrt{-1}$

2013 2015 2017 2016 2014

1 solution

Sagar Shah
Nov 27, 2015

We know that, w^3 = i ^4 = 1..

So, w^12 = i^12 because LCM of 3 & 4 is 12.

So we can conclude that x is equal to 12 or a multiple of 12...

Hence, 2016 is the answer as 2016|12.