Complex Numbers and Trigonometric Functions

The video tutorial explains how to find the three complex roots of the equation z^3 = 8i using Euler's formula. It covers plotting the complex number on the coordinate plane, calculating the modulus, finding coterminal angles, and converting to exponential form. The tutorial then demonstrates how to find the cube roots by evaluating trigonometric values and converting back to polar form, resulting in three complex solutions.

What is the main goal when using Euler's formula in this context?

• To find the three complex solutions of z cubed equals 8i

• To determine the real part of a complex number

• To find the modulus of a complex number

• To convert a complex number to Cartesian form

What is the modulus of the complex number 8i?

• 4

• 8

• 16

• 2

What is the least positive coterminal angle for the complex number 8i?

• 0 radians

• π/2 radians

• 2π radians

• π radians

How many exponential forms are needed to find the cube roots of 8i?

• Four

• Three

• Two

• One

What is the cube root of 8 in the context of finding z sub 1?

• 1

• 2

• 4

• 8

What is the cosine of π/6 radians?

• 1/2

• 0

• 1

• √3/2

What is the sine of 5π/6 radians?

• 1/2

• -1/2

• √3/2

• -√3/2

What is the complex solution for z sub 2?

• -2i

• 2i

• -√3 + i

• √3 + i

What is the cosine value for the angle 3π/2 radians?

• -1

• 0

• 1

• 1/2

What is the third complex solution or root?

• √3 + i

• -√3 + i

• -2i

• 2i