Complex Numbers/Solving Quadratics by Completing the Square

Presentation

•

Mathematics

•

12th Grade

•

Medium

•

CCSS

HSN.CN.A.2, HSN.CN.A.1, HSA-REI.B.4B

Standards-aligned

Abby Kennedy

Used 8+ times

FREE Resource

8 Slides • 9 Questions

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

Multiple Choice

What is the imaginary number in this number:

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

Multiple Choice

Try subtraction!

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

-3i

5 - 8i

9 - 4i

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)

16i

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)

Complex Numbers

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