Understanding Powers of i

The video tutorial explains how to simplify powers of the imaginary unit i. It starts with basic powers of i, such as i^0, i^1, i^2, and i^3, and then introduces a method to simplify higher powers by expressing them in terms of i^4. The tutorial provides examples, including i^23, i^72, i^37, and i^46, demonstrating the process of dividing the exponent by 4 to find the quotient and remainder, which helps determine the simplified form of the power.

What is the value of i raised to the power of 2?

• -i

• i

• -1

• 1

How does i^4 simplify?

• 1

• i

• -i

• -1

What is the first step in simplifying i raised to a high power?

• Subtract 4 from the exponent

• Divide the exponent by 4

• Multiply by 4

• Add 4 to the exponent

If the remainder is 1 when dividing the exponent by 4, what does i^n simplify to?

• i

• 1

• -i

• -1

What is the simplified form of i^23?

• 1

• -i

• i

• -1

What is the remainder when 72 is divided by 4?

• 2

• 1

• 3

• 0

What does i^72 simplify to?

• -i

• -1

• i

• 1

What is the simplified form of i^37?

• 1

• i

• -1

• -i

What is the remainder when 46 is divided by 4?

• 3

• 2

• 0

• 1

What does i^46 simplify to?

• 1

• i

• -1

• -i