Complex Numbers

​Complex Numbers and Operations

​​Objective: Students will review the definition of complex numbers and learn how to perform operations on complex numbers.

VOCABULARY

Real Numbers: a number that can be found on a number line.

​VOCABULARY

​EXAMPLE

Multiple Choice

How do you write the following number using the imaginary unit i? $$\sqrt[]{-12}$$

• $$i\ \sqrt[]{12}$$

• $$2i\ \sqrt[]{3}$$

• $$-\sqrt[]{12}$$

• 7

Multiple Choice

How do you write the following number by using the imaginary unit i? $$\sqrt[]{-25}$$

• i

• 5

• -5

• 5i

Multiple Choice

How do you write the following number by using the imaginary unit i? $$\sqrt[]{-7}$$

• i

• -7

• $$i\ \sqrt[]{7}$$

• no answer

VOCABULARY

Complex Numbers: a combination of real and imaginary numbers (Cannot be found on a number line).

Adding Complex Numbers

When adding complex numbers, combine like terms

1. Add real parts together (any numbers without an i attached to it)
2. Add imaginary parts together (any numbers with an i attached to it)

​Adding Complex Numbers

​Find the sum of the following:

(5 + 2i) + (4 - 8i)

​Identify like-terms (real numbers together & imaginary numbers together)

Combine like-terms


Solution

Multiple Choice

Find the Sum

3i + 2i

• 5i

• 5i²

• 6i

• -5

Multiple Choice

Find the sum. combine the like terms

(5-2i) + (-7+8i)

• -2+6i

• 12+6i

• -35-16i²

• -35 -16i

Subtracting Complex Numbers

​(3 + 2i) - (8 - 4i)

​Distribute the negative

​3 + 2i - 8 + 4i

​Identify like-terms

​

​3 + 2i - 8 + 4i

​

-5 + 6i

Solution

Multiple Choice

Simplify:

(10+ 15i) - (48 - 30i)

• 58 - 45i

• 58 - 15i

• -38 - 15i

• -38 + 45i

​Multiplying Complex Numbers

​Multiply 3 and 4, and the i's 

Replace i² with -1

Simplify

​Multiply 5 and -6, and the i's 

Replace i² with -1

Simplify

​Multiplying Complex Numbers

​Distribute 3i

Replace i² with -1

Simplify

Multiple Choice

Find the product: $$\left(-2i\right)\left(-6+i\right)$$

• 2+12i

• 12i

• no answer