Complex Numbers and Their Operations

The video tutorial covers simplifying rational expressions by factoring and cancellation, multiplying and simplifying algebraic expressions, and simplifying polynomial expressions through factoring and division. It also explores complex numbers, their properties, and graphical representation on the complex plane.

What is the simplified form of the expression 4x^2 - 16 over 2 - x?

• -4(x + 2)

• 4(x + 2)

• 4(x - 2)

• -4(x - 2)

When simplifying the expression (x^2 + 4x)/(x + 3) * (x^2 - 9)/(x^2 + x - 12), what is the result?

• x + 3

• x^2

• x

• 1

What is the simplest form of the expression (5x^3y + 20x^2y^2 + 20xy^3) / 5xy?

• x^2 + 4xy + 4y

• x^2 + 4xy + y^2

• x^2 + 4x + 4

• x^2 + 4xy + 4y^2

Which point on the complex plane represents the number 5 - 2i?

• Point C

• Point D

• Point A

• Point B

What is the value of i^4?

• -1

• 0

• 1

• i

If i is the square root of -1, what is i^2?

• -1

• 1

• 0

• i

Which of the following complex numbers is represented by the point (3, -4) on the graph?

• -3 - 4i

• -3 + 4i

• 3 - 4i

• 3 + 4i

What is the result of multiplying i by itself?

• i

• 0

• -1

• 1

How do you represent the imaginary unit i on the complex plane?

• On the z-axis

• At the origin

• On the y-axis

• On the x-axis

What is the real part of the complex number 3 - 4i?

• -4

• 4

• 3

• 0