Complex Numbers and Their Properties

The video tutorial explains how to find the four complex roots of the equation c^4 = -64 using Euler's formula. It covers plotting the complex number on the coordinate plane, calculating the modulus, finding coterminal angles, and converting to exponential and polar forms. The tutorial concludes with evaluating trigonometric values to express the roots in the form x + yi.

What is the main goal of the problem discussed in the video?

• To plot -64 on a real number line

• To convert -64 into a fraction

• To find the four complex solutions for c^4 = -64

• To find the square root of -64

What does Euler's formula express a complex number as?

• x + yi

• r * e^(iθ)

• c * d^(iθ)

• a + bi

What is the modulus of the complex number -64?

• 128

• 64

• 16

• 32

What is the first angle in standard position for the complex number -64?

• 270 degrees

• 90 degrees

• 0 degrees

• 180 degrees

How many least positive coterminal angles are used in this problem?

• Two

• Three

• Four

• Five

What is the fourth root of 64?

• 2√2

• 4

• 8

• 16

What is the polar form of a complex number?

• r * (cosθ + i sinθ)

• a + bi

• x + yi

• r * e^(iθ)

What is the value of θ for z1 in the polar form?

• 1/4 π

• 1/2 π

• 5/4 π

• 3/4 π

Which of the following is a complex solution for z2?

• 2 + 2i

• -2 + 2i

• 2 - 2i

• -2 - 2i

How can the complex solutions be verified?

• By using a calculator in degree mode

• By using a calculator in radian mode and complex mode

• By plotting them on a real number line

• By converting them into fractions