Algebra 2 Final Review Complex #'s Quadratic Equations

Algebra 2 - Lesson Powers of i

by Scott Madeoy

Multiple Choice

What is the remainder?

$$\frac{25}{4}$$  

• 0

• 1

• 2

• 3

Multiple Choice

$$i^3=?$$  

• 1

• i

• -i

• -1

Multiple Choice

$$i^4=?$$  

• 1

• i

• -i

• -1

Multiple Choice

Simplify.

$$i^{15}$$  

• 1

• -1

• i

• -i

Multiple Choice

Simplify.

$$i^{22}$$  

• 1

• -1

• i

• -i

Complex Numbers

Learning Target: I can simplify expressions with complex numbers.

Adding Complex Numbers

• When adding complex numbers

  -Add real parts together

  -Add imaginary parts together

Multiple Choice

Find the Sum

3i + 2i

• 5i

• 5i²

• 6i

• -5

Multiple Choice

Find the sum.

(5-2i) + (-7+8i)

• -2+6i

• 12+6i

• -35-16i²

• -35 -16i

Subtracting Complex Numbers

• Distribute the negative

• Add real parts together

  Add imaginary parts together

Multiple Choice

Simplify:

(10+ 15i) - (48 - 30i)

• 58 - 45i

• 58 - 15i

• -38 - 15i

• -38 + 45i

Multiplying Complex Numbers

• Use an area model.

• Multiply to get insides

• Add like terms

• simplify i²

• Write as a sum

Multiple Choice

(2i)(3i)

• 5i

• -5

• 6i

• -6

Multiple Choice

Simplify:
-3i(4 + 2i)

• 6 - 12i
• 6 + 12i
• -12i - 6i²
• -12i + 6i²

Multiple Choice

Simplify:
(2 - 3i)(5 + 4i)

• 22 - 7i
• 22 + 7i
• 22 - 7i²
• 22 + 7i²

Multiple Choice

Simplify
(-6 - 2i)²

• 32
• 36-4i
• 36+24i
• 32+24i

The quadratic x²+2x-3=0​

in factored form is (x+3)(x-1) =0

*Set each factor equal to 0 and solve

x+3 = 0 and x-1 = 0 ​

-3 -3 +1 +1

x = -3 x = 1​

​Example

To find the solutions (sometimes called roots or zeros):

• Set ea​ch factor equal to 0

• Solve for x.​

​Solving (finding solutions)

​Factoring Remediation

​The solutions are x = -3 and x = 1

Multiple Choice

What equations would I use to solve x² + 9x - 36 =0

• x + 12 = 0

  and x - 3 = 0

• x + 9 = 0

  and

  x - 4 = 0

• x - 12 = 0

  and

  x + 3 = 0

• x² + 9 = 0

  and

  x - 36 = 0

Multiple Choice

What equations would I use to solve x² + 14x - 32 =0

• x + 16 = 0

  and x - 2 = 0

• x + 7 = 0

  and

  x - 7 = 0

• x - 16 = 0

  and

  x + 2 = 0

• x² + 14 = 0

  and

  x - 32 = 0

Multiple Choice

Convert x² - 9x + 20 = 0 to factored form and solve.

• (x-10)(x+2)=0

  x = -2, 10

• (x+4)(x+5)=0

  x = -5, -4

• (x-4)(x-5)=0

  x = 4, 5

• Not factorable

Multiple Choice

Solve

x² + 2x - 20 = 4

• x = -6, x = 4

• x = 6, x = -4

• x = 12, x = -2

• x = 8, x = -3

The Quadratic Formula:

Directions of using quadratic formula.

Multiple Select

Solve using quadratic formula.

• 0

• 3

• -3

• -2

Multiple Select

Solve using quadratic formula.

(hint: equation must be in standard form) $$y=ax^2+bx+c$$

• $$\frac{8}{3}$$

• $$2$$

• $$1$$

• $$1$$

• $$-\frac{3}{8}$$

Multiple Choice

Identify a, b and c in the quadratic equation: $$2x^2-3x-5=0$$  

• a = 2 , b = 3, c = -5

• a = 2, b = -3, c = 5

• a = 2, b = -3, c = -5

• a = -2, b = 3, c = 5

Multiple Choice

Solutions of a quadratic equation are also called

• roots

• x-intercepts

• zeros

• All of the above

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

Solve using the quadratic formula.

$$r^2-2r+4=0$$  

• $$\left\{1\right\}$$  

• $$\left\{1+i\sqrt[]{3},\ 1-i\sqrt[]{3}\right\}$$  

• $$\left\{1.618,\ -0.618\right\}$$  

• $$\left\{\frac{1+i\sqrt[]{3}}{2},\ \frac{1-i\sqrt[]{3}}{2}\right\}$$