Simplify i^12

Problem

i12

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 since the powers of i repeat every four terms.

12÷4=3* remainder *0

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

i12=(i4)3

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

i12=(1)3

5. Simplify the result.

1=1

Final Answer

i12=1

Want more problems? Check here!