Simplify i^51

Problem

i51

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.

51÷4=12* remainder *3

3. Rewrite the expression using the property of exponents in=i(4*k+r)=(i4)k⋅ir

i51=i(4*(12)+3)

4. Substitute i4=1 into the expression.

i51=(i4)12⋅i3

i51=(1)12⋅i3

5. Simplify the result using the known value of i3

i51=1⋅(−i)

i51=−i

Final Answer

i51=−i

Want more problems? Check here!