Complex Numbers & Solving Quadratics Equations Review

-3 + 2i

(-1 + 5i) + (-2 - 3i)

12

(-2 - 2i)(-3 + 3i)

-118 + 34i

(-4 + 6i)(2 - i)(3 + 7i)

2-2i

(-4+i) + (6-3i)

11 + 23i

(1 + i)(2 + 3i)(4 - 3i)

-5+4i

(3+2i)+(1+4i)(2i)

5 + 4i

(4 + 6i) - (-1 + 2i)

-1-13i

(4-3i) - (5+10i)

-33-56i

(4-7i)²

4 + 4i

(6+i) - (2-3i)

30

(6-3i)(4+2i)

2-i

(9-6i) - (7-5i)

6

-3i × 2i

-72√3

3√-24 × 2√-18

Stretched Vertically

Choose one correct transformation for the function below. y = -4(x + 3)² + 21

Compressed Vertically

Choose one correct transformation for the function below. y = 1/3(x)² + 5

Translate left 4 units

Choose one correct transformation for the function below. y = 3(x + 4)² + 3

Translate up one unit

Choose one correct transformation for the function below. y = 9(x - 6)² +1

1 Rational, Real Root

Describe the number and type of roots for the quadratic equation. -16x² + 8x -1 = 0

2 Complex Roots

Describe the number and type of roots for the quadratic equation. 2x² - 6x + 9 = 0

2 Irrational, Real roots

Describe the number and type of roots for the quadratic equation. 3x² + 8x + 2 = 0

True

Every complex number has a real part.

True

Every complex number has an imaginary part.

False

Every complex number has either a real part or an imaginary part.

-19

Find the value of the discriminant for the quadratic equation. 7x² + 11x + 5 = 0

0

Find the value of the discriminant for the quadratic equation. x² + 22x + 121 = 0

3, -2

Find the values of (a) and (b) that make the equation true. 3a + (4b + 2)i = 9 - 6i

5, 3

Find the values of (a) and (b) that make the equation true. 4b - 5 + (-a - 3)i = 7 - 8i

x = 1, -3

Solve by Completing the Square. x² + 2x - 3 = 0

x = -2 ± √2

Solve by Completing the Square. x² + 4x + 2 = 0

x = -2, -5/2

Solve by Completing the Square. 2x² + 9x + 10 = 0

x = -4

Solve by Completing the Square. 2x² = -16x - 32

x = 1, -2.5

Solve using the Quadratic Formula. 2x² + 3x - 5 = 0

x = 1/5, 7

Solve using the Quadratic Formula. 5x² - 36x + 7 = 0

x = (-1 ± i√39) / 4

Solve using the Quadratic Formula. 2x² + 5 = -x

x = (3 ± i√7) / 4

Solve using the Quadratic Formula. 2x² - 3x + 2 = 0

x = (-1 ± i√79) / 8

Solve using the Quadratic Formula. 4x² + x + 5 = 0

x = -4 ± 2√13

Solve using the Square Root Property. (4 + x)² - 5 = 47

x = 1 ± √13

Solve using the Square Root Property. (x - 1)² = 13

x = ± √5 / 2

Solve using the Square Root Property. 4x² - 5 = 0

a + bi

Standard form for a complex number is __________?

y = -2(x - 2)² + 3

Write the function in vertex form. y = -2x² + 8x - 5

y = -(x + 2)² + 3

Write the function in vertex form. y = -x² -4x - 1

1

i raised to the 40th power.

i

i raised to the 41th power

-4√15

√-10 × √-24

2i√6

√12 × √-2