Simplify i^4

Problem

i4

Solution

1. Identify the definition of the imaginary unit i where i2=−1

2. Rewrite the expression using the laws of exponents to express i4 in terms of i2

i4=(i2)2

3. Substitute the value of i2 into the expression.

i4=(−1)2

4. Evaluate the square of −1

(−1)×(−1)=1

Final Answer

i4=1

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