Simplify i^56

Problem

i56

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.

56÷4=14

3. Determine the remainder of the division. Since 56 is exactly divisible by 4, the remainder is 0.

56=4×14+0

4. Apply the power rule for exponents to rewrite the expression using the remainder.

i56=(i4)14

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

1=1

Final Answer

i56=1

Want more problems? Check here!