Math 10 Complex Conjugate and Quotients

Learning Targets

• I can multiply complex numbers. 

• I can identify the complex conjugate of a complex number. 

• I can simplify a quotient with complex numbers.

Recall: Using the "imaginary" unit in problem-solving.

Recall: Adding/Subtracting complex numbers

Nothing too crazy.

Multiple Choice

Recall that the value of  $$i=\sqrt{-1}$$   . What is the value of  $$i^2$$  ?

• 1

• -1

• 2

• 0

Multiple Choice

Simplify the expression: $$i\left(i+2\right)$$  

• $$i+2i$$  

• $$-1+2i$$  

• 3

Multiple Choice

Simplify the expression: $$i\left(2i\right)$$  

• $$2i$$  

• $$-1+2i$$  

• -2

Important to Remember

Multiple Choice

Simplify the expression:
$$\left(1+2i\right)\left(1-2i\right)$$  

Hint: Use the distributive property!

• $$1-4i^2$$  

• $$2$$  

• $$5$$  

Multiple Choice

Identify the complex conjugate:

$$1+2i$$  

• $$1+2i$$  

• $$1-2i$$  

• $$i^2$$  

• $$-1+2i$$  

Multiple Choice

Identify the complex conjugate:

$$2-3i$$  

• $$2+3i$$  

• $$2-3i$$  

• $$i^2$$  

• $$-2-3i$$  

Why the complex conjugate?

Why the complex conjugate?

Important Note

Multiplying by the complex conjugate does NOT change the quotient/fraction. It simply creates an equivalent fraction.

Let's try one more together

Debrief

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

What is the conjugate of -5 + 4i

• 5 + 4i

• 5 - 4i

• -5 - 4i

• -5 + 4i

Multiple Choice

What is the conjugate of 4i?

• 4i

• 4 + 4i

• 4-4i

• -4i

To divide complex numbers

Multiply the top and bottom by the conjugate of the denominator

Multiple Choice

Simplify

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

• A
• B
• C
• D

Multiple Choice

Use what you know about complex conjugates to determine the conjugate of $$2+\sqrt[]{3}$$  .

• $$2+\sqrt[]{3}$$  

• $$2-\sqrt[]{3}$$  

• $$-2+\sqrt[]{3}$$  

• $$-2-\sqrt[]{3}$$