Simplify i^63

Problem

i63

Solution

1. Identify the cycle 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 find the remainder. We calculate 63÷4

3. Determine the quotient and remainder. Since 4×15=60 we have:

63=4*(15)+3

4. Apply the property of exponents to rewrite the expression.

i63=i(4*(15)+3)

i63=(i4)15⋅i3

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

i63=(1)15⋅(−i)

6. Simplify the final result.

i63=1⋅(−i)

i63=−i

Final Answer

i63=−i

Want more problems? Check here!