## How - imaginary number i raised to large powers

Here is a very fast method to simplify the imaginary number i raised to a large positive whole number power. For problems looking like: i^397

Step 1 - divide the power by four in a calculator.

Step 2 -

Step 1 - divide the power by four in a calculator.

Step 2 -

- If the answer in step 1 is a whole number, your answer is "1"
- If the answer in step 1 is a decimal ending with .25, your answer is "i"
- If the answer in step 1 is a decimal ending with .5, your answer is "-1"
- If the answer in step 1 is a decimal ending with .75, your answer is "-i"

## Quick Example

So for i^397

Step 1 - Type 397/4 into a calculator. We get 99.25

Step 2 - because that answer was a decimal ending with .25, that means i^397 = -i

Step 1 - Type 397/4 into a calculator. We get 99.25

Step 2 - because that answer was a decimal ending with .25, that means i^397 = -i