Complex Numbers in Trigonometric Form

This video tutorial explains how to multiply and divide complex numbers in trigonometric form. It begins with an introduction to the multiplication of complex numbers, detailing the process of multiplying magnitudes and adding angles. An example is provided to illustrate the steps. The video then transitions to dividing complex numbers, explaining the use of the conjugate to simplify the process. The tutorial concludes with an example of division, demonstrating the ease of using trigonometric form over rectangular form.

What is the first step in multiplying two complex numbers in trigonometric form?

• Subtract the angles

• Multiply the magnitudes

• Divide the magnitudes

• Add the angles

Which identity is used to simplify the product of two complex numbers in trigonometric form?

• Tangent identity

• Double angle identity

• Cosine and sine sum identities

• Pythagorean identity

In the example, what is the result of multiplying 2 and 3 in the trigonometric form?

• 5

• 6

• 8

• 9

What is the reference angle used in the multiplication example?

• 45 degrees

• 60 degrees

• 90 degrees

• 30 degrees

What is the key step in deriving the formula for dividing complex numbers in trigonometric form?

• Using the Pythagorean identity

• Multiplying by the conjugate of the denominator

• Adding the angles

• Subtracting the angles

What happens to the denominator when multiplying by the conjugate in the division of complex numbers?

• It becomes zero

• It doubles

• It halves

• It becomes one

In the division example, what is the result of dividing 24 by 6?

• 2

• 3

• 5

• 4

What is the reference angle used in the division example?

• 90 degrees

• 60 degrees

• 30 degrees

• 45 degrees

What is the cosine of 120 degrees used in the division example?

• -Square root of 3/2

• 1/2

• -1/2

• Square root of 3/2

What is the sine of 120 degrees used in the division example?

• 1/2

• -Square root of 3/2

• -1/2

• Square root of 3/2