Download Algebra 2 Notes ~ Lesson 5.6 Review Imaginary Numbers/Complex Numbers

Algebra 2 Notes ~ Lesson 5.6
Review: Simplify the Following Radicals
1.
20
2.
3. 18
72
4.
90
5. 125
Imaginary Numbers/Complex Numbers:
An Imaginary Unit is defined as:
The square root of any negative number is defined as follows:
Examples: Simplify the following radicals using imaginary numbers:
1.
16  _______
2.
100  _______
3.
12  _______
Complex Numbers are written in the form: _________________________
Graphing Complex Numbers:
(3 - 4i) is graphed like (3, -4)
4.
54  _______
Absolute Value:
The absolute value of a complex number is the distance from the origin on the complex number plane
1. Find 3  4i
2. Find 2  5i
4. Find 6  4i
3. Find 4i
Additive Inverse:
1. -2 + 5i
2. -5i
3. 4-3i
4. -3 - 2i
5. -4 + 7i
Adding/Subtracting Complex Number: Simplify each expression.
REMEMBER: ONLY ADD LIKE TERMS
1. (5 + 7i) + (-2 + 6i)
2. (8 + 3i) – (2 + 4i)
3. 7 – (3 + 2i)
4. (4 - 6i) + 3i
Multiplying Complex Numbers: Simplify each expression. REMEMBER: i 2  1
1. (5i)(-4i)
2. (12i)(7i)
3. (2 + 3i)(-3 + 5i)
Finding Complex Solutions: Solve each equation.
1. 4 x 2  100  0
2. 3x 2  48  0
4. x 2  7
5. 5 x 2  3  0
3. 3x 2  2  62
4. (4 – 9i)(4 + 3i)