Trigonometric Functions and Complex Numbers

The video tutorial explains how to use De Moivre's Theorem to find the 5th power of a complex number given in polar form. It begins with an introduction to complex numbers and the theorem, followed by a step-by-step application of the theorem. The unit circle is used to determine trigonometric values, and the result is simplified. The tutorial concludes with a mention of an alternative method using the exponential form of complex numbers.

What is the initial form of the complex number given in the problem?

• Exponential form

• Polar form

• Trigonometric form

• Rectangular form

According to De Moivre's Theorem, what is the expression for Z to the Nth power?

• R to the Nth power times cosine of N times theta plus I sine of N times theta

• R times cosine of N times theta plus I sine of theta

• R times cosine of theta plus I sine of theta

• R to the Nth power times sine of N times theta

What is the value of 2 to the 5th power in the context of this problem?

• 32

• 128

• 64

• 16

What is the cosine value of 5PI/6 radians?

• 1/2

• -1/2

• -√3/2

• √3/2

What is the sine value of 5PI/6 radians?

• -1/2

• 1/2

• -√3/2

• √3/2

What is the simplified form of the complex number raised to the 5th power?

• 32√3 + 32I

• -16√3 + 16I

• 16√3 + 16I

• -32√3 + 32I

What alternative method is mentioned for solving the same problem?

• Using the rectangular form

• Using the exponential form

• Using the algebraic form

• Using the logarithmic form