Exploring Operations with Complex Numbers

This video tutorial covers the basics of complex numbers, including their definition as a combination of real and imaginary numbers. It explains how to perform operations such as addition, subtraction, and multiplication with complex numbers. The tutorial also demonstrates how to graph complex numbers on a real and imaginary axis. Additionally, it explores the properties of the imaginary unit i, including how to simplify its powers using a repeating pattern.

What is the imaginary unit 'i' equal to?

• The square root of -1

• The square root of 2

• The square root of 0

• The square root of 1

How do you add complex numbers?

• Multiply the real parts and add the imaginary parts

• Subtract the real parts and add the imaginary parts

• Combine the real parts and the imaginary parts separately

• Combine the real parts and subtract the imaginary parts

What is the result of 5 + 2i + 3 - 7i?

• 8 - 5i

• 2 + 5i

• 2 - 5i

• 8 + 5i

How do you graph the complex number 2 + 3i?

• Go 2 units left and 3 units down

• Go 2 units right and 3 units up

• Go 2 units up and 3 units right

• Go 2 units down and 3 units left

What is the complex number represented by the point (0, -3) on the graph?

• -3i

• -3

• 3i

• 3

What is the result of multiplying 4 by 3 - i?

• 12 + 4i

• 12 - 4i

• 12 - 3i

• 12 + 3i

What is the result of (2 + 3i)(1 - i)?

• 5 + i

• 5 - i

• 5 + 2i

• 5 - 2i

What is the value of i squared?

• 1

• -i

• i

• -1

What is the value of i to the 16th power?

• -i

• -1

• 1

• i

What is the value of i to the 39th power?

• 1

• -1

• -i

• i