Simplify i^36

Problem

i36

Solution

1. Identify the cycle of powers of the imaginary unit i

i1=i

i2=−1

i3=−i

i4=1

2. Determine the remainder when the exponent is divided by 4, as the powers of i repeat every 4 terms.

36÷4=9* remainder *0

3. Rewrite the expression using the property of exponents (am)n=a(m*n) to isolate the i4 term.

i36=(i4)9

4. Substitute the known value i4=1 into the expression.

i36=(1)9

5. Simplify the result by calculating the power of 1.

1=1

Final Answer

i36=1

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