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Evaluate:i, to the power 90i 90

Question

Evaluate:i, to the power 90i 90

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Solution

The question seems to be asking for the value of i raised to the power of 90. In mathematics, "i" is the imaginary unit, which is defined as the square root of -1.

Here are the steps to solve this:

  1. We know that i to the power of 1 is i, i to the power of 2 is -1, i to the power of 3 is -i, and i to the power of 4 is 1. This pattern repeats every 4 powers.

  2. To find i to the power of 90, we need to find the remainder when 90 is divided by 4, because the powers of i repeat every 4.

  3. The remainder when 90 is divided by 4 is 2.

  4. Therefore, i to the power of 90 is the same as i to the power of 2, which is -1.

So, i to the power of 90 equals -1.

This problem has been solved

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