Simplify i^1002

Problem

i1002

Solution

1. Identify the cycle 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. We calculate 1002÷4

3. Determine the remainder. Since 1000 is divisible by 4, 1002=4×250+2 The remainder is 2.

4. Apply the property of powers of i The expression in is equivalent to ir where r is the remainder of n÷4

5. Evaluate the simplified power.

i1002=i2

i2=−1

Final Answer

i1002=−1

Want more problems? Check here!