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Evaluate the expression i^105 and write the result in the form a + bi. The real number a equals The real...

Evaluate the expression i^105 and write the result in the form a + bi.
The real number a equals
The real number b equals

Answer

i^105 can be simplified using the cyclical nature of powers of i:

  1. i^1 = i
  2. i^2 = -1
  3. i^3 = -i
  4. i^4 = 1

Since the powers of i repeat every 4, we find the remainder of 105 divided by 4, which is 1. Therefore, i^105 = i^1 = i.

The result in the form a + bi is:

  1. The real number a equals 0.
  2. The real number b equals 1.

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