Simplify i^60

Problem

i60

Solution

1. Identify the cycle of the powers of the imaginary unit i The powers of i repeat every four terms: i1=i i2=−1 i3=−i and i4=1

2. Divide the exponent by 4 to determine the position in the cycle. We calculate 60÷4

3. Determine the remainder of the division. Since 60=4×15+0 the remainder is 0

4. Apply the rule for powers of i Any power in where n is a multiple of 4 (remainder 0) is equivalent to i4

5. Evaluate the expression. Since the remainder is 0 i60=(i4)15=1=1

Final Answer

i60=1

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