Tutorial - Simplifying an imaginary given to a higher power ex 6, i^85

The video tutorial explains how to simplify an imaginary number raised to a higher power. It covers the concept of imaginary numbers and their powers, highlighting the repetition pattern every fourth power. The tutorial demonstrates how to calculate the division and remainder to simplify i to the 85th power, concluding that it equals i.

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

• -1

• 1

• -i

• i

How many times does the cycle of powers of 'i' repeat in i^85?

• 21 times

• 20 times

• 23 times

• 22 times

What is the remainder when 85 is divided by 4?

• 0

• 1

• 2

• 3

If i^85 is simplified using the cyclical pattern, what is the result?

• 1

• -i

• i

• -1

Which of the following is true about the powers of 'i'?

• i^4 = 1

• i^2 = i

• i^3 = 1

• i^4 = -1