Complex Numbers and Imaginary Units

The video tutorial explains how to multiply complex numbers algebraically, ensuring the product is in the form of a complex number. It provides examples, such as multiplying 5i and -6i, distributing -4i with 3 - 7i, and calculating 3i cubed. The tutorial also demonstrates how to verify these calculations using a graphing calculator in complex mode.

What is the correct form of a complex number?

• a + b

• a + bi

• a - bi

• a - b

What is the value of i squared?

• 0

• 1

• i

• -1

What is the product of 5i and -6i?

• -30

• 30

• -30i

• 30i

What is the result of distributing -4i over (3 - 7i)?

• 12i - 28i^2

• -12i + 28i^2

• 12i + 28

• -12i - 28

What is the simplified form of -28i^2?

• -28

• -28i

• 28i

• 28

What is the product of 3i cubed?

• -27i

• 27i

• -27

• 27

What is the simplified form of 27i^3?

• -27

• 27

• -27i

• 27i

What mode should the graphing calculator be in to verify complex number products?

• Real mode

• Complex mode

• Imaginary mode

• Standard mode

Which key is used to access the imaginary unit 'i' on the graphing calculator?

• Second + Exponent

• Second + Mode

• Second + Enter

• Second + Decimal Point

What is the result of 3i raised to the third power on the graphing calculator?

• 27i

• -27i

• -27

• 27