Unit 1B: Quadratics Revisited

2017

pebblebrook high schoolALGBRA 2

1B.1 – 1B.6

1B.1 Simplifying Radicals

Pairs Come Out √Not Paired

Example: Simplify

1) √49 3) √48

2) 3√72 4) −√128

Section 1B.1 Homework

1B.2 Operations w/ Complex Numbers

Fact: i2= -1

Example 1: Simplify

a) √−8

b) √−2

c)√−12

√−36

Example 2: Write the complex number in the form a + bi

a)√−9 + 6

b) −√−16 + 7

Example 3: Adding & Subtracting Complex Numbers

a) (5 + 7i) + (-2 + 6i)

b) (8 +3i) – (2 + 4i)

c) 7 – (-3 + 2i)

d) (4 – 6i) + 3i

Section 1B.2 Homework Simplify

1) √−7 2) √−15 3) √−81 4) √−32

Write in the form of a + bi

1) 2 + √−3 6) √−8 + 8

2) 6 - √−28 7) - √50 – 2

Simplify each expression

3) (2 + 4i) + (4 – i) 8) (-3 – 5i) + (4 – 2i)

4) (7 + 9i) + (-5i) 9) 6 – (8 + 3i)

5) (12 + 5i) – (2 – i) 10) (-6 – 7i) – (1 + 30)

1B.3 Powers of iRemember i2 = -1, so….

Challenge… Simplify (5 + 2i) – (3 + i)2

Section 1B.3 Homework

1)i2

2)i6

3)i3

4)i5

5)i7

6)i9

7)i12

8)i15

Section 1B.4 Solving Quadratics w/ Complex Solutions

Examples: Finding Complex Solutions

1) 4x2+ 100 = 0

2) 3x2+ 48 = 0

3) -5x2 – 150 = -200

4) 2x2 = -6x – 7

Section 1B.4 Homework

Section 1B.5 Dividing Complex Numbers

Example 1: Write the conjugate of the complex number.

1) 5 – 2i 3) -7i

2) 6 + 3i 4) 8i

Diving Complex Numbers

Identify the conjugate of the DENOMINATOR!

Multiply BOTH numerator AND denominator by the conjugate.

Simplify both numerator AND denominator!

Example 2: Divide

1) 2−3 i4 i

2) 1+7ii

3) −4+2i1−4 i

Section 1B.5 Homework

Section 1B.6 More Complex Numbers

Graphing Complex Numbers

Example 1: Graph the Complex Number

1) 5i

The y-axis becomes the IMAGINARY AXIS. The x-axis becomes the REAL

AXIS.

3 – 4i

2) -3

3) 2 + 2i

4) -5 – 3i

Modulus of a Complexa.k.a. The Absolute Value of a Complex Number…..

Remember, a is the real number & b is the coefficient of i.

Example 2: Find the modulus.1)5i

2) -3

3) 2 + 2i

4) -5 – 3i

Section 1B.6 Homework