What is the ith root of i?

This is what I will be attempting to quantify today

Some Basic Rules

This is where I explain some basic rules for simplification. If you already are familiar with basic exponent rules, the rules about integral powers of i (i stands for iota, which is the imaginary unit with the value of i=√-1 and is the solution to x²+1=0), and the Euler form of complex numbers, feel free to skip ahead to where I solve this problem.

The basic exponent rule of root-power equivalence.
A basic exponent rule.
Euler form of complex number Z, where Θ is the argument of Z.

The Working

Now that we know some basic rules, let us find out what the ith root of i is. First off we apply the root-power equivalence to simplify the expression.

Using the root-power equivalence, we have converted this into fractional form
We have rationalized the powers
A simplified version of the original problem

Some interesting things to keep in mind

If you’ve read it this far with a lot of concentration, you must have noticed that there were some number power patterns on some statements. This is where I explain what they mean.



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