Simplifying High Powers of I

This video tutorial explains how to simplify high powers of the imaginary number i by identifying a repeating pattern in its lower powers. The instructor demonstrates that the powers of i repeat every four terms and shows how to use remainders to simplify large powers, such as i to the 623. By dividing the exponent by four and finding the remainder, one can determine the simplified form of any power of i.

What is the imaginary number i equal to?

• The square root of 0

• The square root of 1

• The square root of -1

• The square root of 2

What is i to the first power?

• 1

• 0

• -1

• i

What is i squared?

• 0

• i

• -1

• 1

What is i to the fourth power?

• i

• -1

• 0

• 1

What is the pattern of powers of i?

• i, -1, -i, 1

• i, -1, i, 1

• 1, -1, i, -i

• i, -i, -1, 1

How do you determine the position of a high power of i within the pattern?

• By dividing the power by 4 and finding the remainder

• By adding 4 to the power

• By subtracting 4 from the power

• By multiplying the power by 4

What is the remainder when 7 is divided by 4?

• 0

• 3

• 2

• 1

What is the remainder when 8 is divided by 4?

• 0

• 3

• 2

• 1

What is the remainder when 623 is divided by 4?

• 0

• 1

• 2

• 3

What is i to the 623rd power?

• -1

• 1

• -i

• i