Complex Numbers and Quadratics

Complex Numbers

First lets talks about the form of Complex Numbers

• a+bi is the standard form on complex numbers

• a is the real part and bi is a pure imaginary number

Multiple Choice

Which is the real part in this number:

5+2i

• 5

• 2

• 2i

• 5+2i

Multiple Choice

What is the imaginary number in this number:

6+3i

• 6

• 3

• 3i

• 6+3i

a+bi are not like terms and cannot be combined!

Lets try adding two complex numbers together.

• (-11+3i)+(9+2i)

Multiple Choice

(4+i)+(7-5i)

• 5i+2i

• 11+6i

• 11-4i

• 7i

Multiple Choice

Try subtraction!

(7-2i) - (2+6i)

• -3i

• 5 - 8i

• 9 - 4i

• 5i

Multiplying Complex Numbers

RECALL:

 $i^2=-1$  
Let's try:
(2-4i)(-5-3i)

Multiple Choice

(7+i)(4-i)

• 29-3i

• 
  

  $$11-i^2$$

• $$28-i^2$$

• 27- 3i

Complex Conjugates

(5-4i)(5+4i)

• Two complex numbersn the form a+bi and a-bi are called complex conjugates.

• The product of two conjugates is always a real number

Multiple Choice

(8+8i)(8-8i)

• 65

• 64

• 16i

• 16

Dividing Complex Numbers

• NOTE: "i" cannot be in the denominator of a complex number!!!

• If the denominator is a monomial: Multiply BOTH numerator and denominator by the monomial

• If the denominator is a binomial: Multiply BOTH numerator and denominator by the conjugate

• Lets try:

   $\frac{10}{2i}$  

Now, lets try this one

 $\frac{-2}{\left(5-i\right)}$  

Multiple Choice

$$\frac{\left(28-8i\right)}{4i}$$  

• 2+7i

• 28-2i

• 7-2i

• -2-7i

Lets try: $x^2-18x+56=0$  

Multiple Choice

$$2x^2-16x+30=0$$  

• {3,5}

• {-3,5}

• {3,-5}

• {-3,-5_

Multiple Choice

$$3x^2+10x+8=0$$  

• (4/3 , 2)

• (4/3, 1/3)

• (-4/3 , -2)

• (1/3, -1/3)