Simplify i^67

Problem

i67

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 find the remainder.

67=4×16+3

3. Rewrite the expression using the properties of exponents.

i67=i(4×16+3)

i67=(i4)16×i3

4. Substitute the known values i4=1 and i3=−i into the expression.

i67=(1)16×(−i)

5. Simplify the final result.

i67=1×(−i)

i67=−i

Final Answer

i67=−i

Want more problems? Check here!