Properties of Imaginary Numbers

The video tutorial explains how to simplify imaginary numbers with large exponents by dividing the last two digits of the exponent by four. The remainder determines the power of I, with I to the power of 0 equaling one, I to the power of 1 equaling i, I to the power of 2 equaling negative one, and I to the power of 3 equaling negative i. The tutorial concludes with a summary of these calculations.

What is the first step in simplifying imaginary numbers with large exponents?

• Multiply the exponent by four

• Divide the last two digits of the exponent by four

• Add four to the exponent

• Subtract four from the exponent

What is the remainder when 32 is divided by 4?

• 0

• 3

• 1

• 2

If the remainder is 0 when dividing the exponent by 4, what is the value of I raised to that power?

• -1

• 0

• i

• 1

What is the result of I to the power of 0?

• i

• 1

• 0

• -1

If the remainder is 1 when dividing the exponent by 4, what is the value of I raised to that power?

• -1

• 1

• 0

• i

What is the result of I to the power of 1?

• 1

• -1

• 0

• i

What is the remainder when 49 is divided by 4?

• 3

• 0

• 2

• 1

If the remainder is 2 when dividing the exponent by 4, what is the value of I raised to that power?

• -1

• i

• 0

• 1

What is the result of I squared?

• i

• 0

• -1

• 1

What is the remainder when 26 is divided by 4?

• 3

• 2

• 0

• 1