Exploring Complex Numbers and the Imaginary Unit

The video tutorial introduces real numbers, imaginary numbers, and complex numbers. It explains the concept of imaginary numbers using the unit 'i', which is defined as the square root of negative one. The tutorial then combines real and imaginary numbers to form complex numbers, represented as a sum of a real part and an imaginary part. The video also demonstrates how to visualize complex numbers on a complex plane, with examples of plotting specific complex numbers.

Which of the following is a real number?

• i

• 3

• 3i

• pi*i

What is the value of i squared?

• 0

• i

• -1

• 1

Which of the following is an example of an imaginary number?

• e

• 2i

• 5

• pi

What do we call a number that has both a real and an imaginary part?

• Rational number

• Complex number

• Imaginary number

• Real number

In the complex number 5 + 3i, what is the real part?

• 5

• i

• 3

• 3i

In the complex number 5 + 3i, what is the imaginary part?

• 3i

• 5

• 3

• i

On the complex plane, what does the horizontal axis represent?

• Angle

• Magnitude

• Real part

• Imaginary part

On the complex plane, what does the vertical axis represent?

• Imaginary part

• Angle

• Real part

• Magnitude

Where would you plot the complex number -2 + i on the complex plane?

• (1, -2)

• (-1, 2)

• (-2, 1)

• (2, -1)

Where would you plot the complex number 4 - 3i on the complex plane?

• (-4, -3)

• (4, 3)

• (4, -3)

• (-4, 3)