Algebra 2 - Review Imaginary/Complex Numbers & Factors

Powers of i

100

Simplify each power of i:

1. i¹

2.i²

3. i³

4. i⁴

What is i, -1, -i, and 1?

200

Simplify i²⁴⁸

What is 1?

300

Simplify i⁷¹⁴

What is -1?

400

Simplify i⁴⁹⁷⁵

What is -i?

500

Simplify i⁴⁰³⁹ x i¹²⁸⁴

What is -i?

Complex Numbers

100

Identify the real and imaginary parts of -12+7i

What is real = -12 and imaginary = 7?

200

Classify -6i as real, imaginary, and/or complex

What is imaginary and complex?

300

Classify 3 - 4i as real, imaginary, and/or complex

What is complex?

400

Describe the process of graphing the complex number -6 + 7i on the complex plane. Be specific!

Where is from the origin, (0, 0), go left 6 and then up 7?

500

State the complex numbers from the descriptions of points A and B below:

A: From the origin, left 5 and down 7

B: From the origin, up 6

What is A = -5 - 7i and B = 6i?

Complex Number Operations

100

Simplify (2+3i) + (4+7i)

What is 6+10i?

200

Simplify (6+5i) - (-3-2i)

What is 9+7i?

300

Simplify (7+i)(7-i)

What is 50?

400

Simplify (2+3i)(4+7i)

What is -13+26i?

500

Simplify -9 + 3i⁹ - 14i⁷ + 16i² - i⁶ - 4i¹²

What is -28 + 17i?

Factoring

100

Factor and find the roots of the equation:

x⁴ - 144 = 0

What is (x² - 12)(x² + 12) = 0?

What is x = +- sqrt 12 and +- i sqrt 12 which can be simplified to x = +-2 root 3 and +-2i roots 3?

Simplified answer +100 bonus

200

Factor and find the roots of the equation:

-6x + 24x⁵ = 0

What is -6x(1+2x²)(1-2x²) = 0 or 6x(-1+2x²)(1+2x²) = 0?

What is x = 0, +- sqrt 1/2, +- i sqrt 1/2?

300

Factor and find the roots for the equation:

x⁶ - x⁴ - 25x² + 25 = 0

What is (x - 1)(x + 1)(x² - 5)(x² + 5) = 0?

What is x = +-1, +- sqrt 5, and +- i sqrt 5?

400

Factor and find the roots for the equation:

x⁴ + 2x² - 48 = 0

What is (x² - 6)(x² + 8) = 0?

What is x = +- sqrt 6 and +-2i sqrt 2?

500

Factor and find the roots for the equation:

x⁷ - 3x⁵ - 25x³ + 75x = 0

What is x(x² - 3)(x² + 5)(x² - 5) = 0?

What is x = 0, +- sqrt 3, +- sqrt 5, +- i sqrt 5?

Quadratic Formula

100

State the purpose of the quadratic formula

What is solving a quadratic equations?

200

Write out the quadratic formula

What is x = (-b +- sqrt of b² - 4ac) / 2a ?

300

Solve:

x² - 6x + 25 = 0

What is x = 3 +- 4i?

400

Solve:

x³ - 2x² + 17x = 0

What is x = 0, 1 +- 4i?

500

Solve:

x³ - 4x² + 8x = 0

What is x = 0, 2 +- 2i?