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- March 11th 2010, 06:41 AM #1

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- March 11th 2010, 06:51 AM #2

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- March 11th 2010, 11:20 AM #6

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I have found it useful when teaching algebra students about the powers of

*i*, is just jot down the following:

Now when encountering any power of*i*, divide the exponent by 4. Using a little modular arithmetic, we arrive at:

[1] If the remainder is 0, then the answer is 1.

[2] If the remainder is 1, then the answer is*i*.

[3] If the remainder is 2, then the answer is -1.

[4] If the remainder is 3, then the answer is -*i*.

Example: because