Algebra 2 - Simplifying complex numbers to a higher power i ^ 81

The video tutorial explains the concept of powers of the imaginary unit 'I', highlighting its cyclical nature. It demonstrates how every fourth power of I resets the cycle, making it easier to calculate higher powers. The tutorial provides a method to determine the power of I using division and remainders, offering examples to illustrate the process.

What is the result of i raised to the 4th power?

• i

• -i

• -1

• 1

How can you simplify the calculation of i raised to a large power, like i^800,001?

• By multiplying i repeatedly

• By using a calculator

• By dividing the exponent by 4 and using the remainder

• By adding the digits of the exponent

What is the equivalent power of i when the exponent is 81?

• 1

• -i

• -1

• i

If the remainder is zero when dividing the exponent by 4, what is the result of i raised to that power?

• i

• -1

• 0

• 1

What is the result of i raised to the 83rd power?

• -1

• 1

• i

• -i