Simplify i^52

Problem

i52

Solution

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

2. Divide the exponent by 4 to determine the remainder.

52÷4=13

3. Determine the remainder of the division. Since 52 is exactly divisible by 4, the remainder is 0.

52=4×13+0

4. Apply the property of exponents to rewrite the expression using the power of a power rule.

i52=(i4)13

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

i52=1

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

1=1

Final Answer

i52=1

Want more problems? Check here!