3/22/23 Complex Numbers

The Set of Complex Numbers

Imaginary Numbers are REAL!

Our idea of the possibilities of numbers was altered this week.

There are more numbers than just the set of Real Numbers that exist.

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