Simplifying Imaginary and Complex Numbers

Complex Numbers: Simplifying & classifying

Learning Target: students will simplify complex expressions using various methods: addition, subtraction, multiplication, & division. Then you will categorize them into the Complex Number System.

​https://youtu.be/T647CGsuOVU

Adding Complex Numbers

• When adding complex numbers

  -Add real parts together

  -Add imaginary parts together

Multiple Choice

Find the sum.

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

• -2+6i

• 12+6i

• -35-16i²

• -35 -16i

Subtracting Complex Numbers

• Distribute the negative

• Add real parts together

  Add imaginary parts together

Multiple Choice

Simplify:

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

• 58 - 45i

• 58 - 15i

• -38 - 15i

• -38 + 45i

Multiplying Complex Numbers

• Distribute

• or use FOIL Method

• Add like terms

• simplify i²

• Write in standard form of complex number ---- a+bi

Multiple Choice

(2i)(3i)

• 5i

• -5

• 6i

• -6

Multiple Choice

(3+8i)(-2-i)

• 2-19i

• 23-i

• 34+5i

• 23-i

Dividing Complex Numbers

​Check your denominator terms

Monomial
vs
binomial

Find the conjugate

The conjugate of a + bi is a - bi

The conjugate of a - bi is a + bi

Multiple Choice

What is the conjugate of 2 + 3i?

• 2 - 3i

• -2 + 3i

• -2 - 3i

• 2 + 3i

Multiple Choice

Simplify.

Multiple Choice

$$\frac{5-8i}{3+2i}$$  , what do you do to divide?

• Multiply the top and bottom by 3-2i

• Multiply the top and bottom by 5 + 8i

• multiply the top by 5 + 8i and the bottom by 3 - 2i

• Multiply the top and bottom by -3 - 2i

Multiple Choice

Solve By Square Roots:

$$5v^2+2=-5$$  

• $$\pm\sqrt{\frac{7}{5}}$$  

• $$\sqrt{\frac{7}{5}}$$  

• $$\pm i\sqrt{\frac{7}{5}}$$  

• $$\pm i\sqrt{\frac{3}{5}}$$  

​The Complex Number System

Closure Property

A set is closed under an operation if applying the operation to elements of the set produces another element of the set

Multiple Choice

Closure property of integers states that if a and b are integers then a + b =c, c is also an integer?

• True

• False

Multiple Choice

True or False:
Integers are closed under division. 

• True
• False

Poll

How do you feel about this lesson?