University:
Henry Ford College
Course:
MATH-115 | College Algebra
Academic year:

2024
Views:

144

Pages:

3
Author:

Hiba N.

Algebra 2 Notes — Part 2 Chapter 7: Radical Equations & Complex Numbers Radical Equations → involve square roots Steps to solve: 1. Isolate the radical 2. Square both sides 3. Solve & check for extraneous solutions!! Example: √(x + 3) = x - 1 → Square both: x + 3 = (x - 1)² → solve that quadratic Complex Numbers: ● i = √-1 ● i² = -1 ● Complex #s: a + bi To simplify: ● Combine like terms ● Multiply using FOIL, and remember: i² = -1 Example: (2 + 3i)(1 - 4i) → 2*1 + 2*(-4i) + 3i*1 + 3i*(-4i) → 2 - 8i + 3i -12i² → 2 - 5i + 12 → 14 - 5i Chapter 8: Exponential & Logarithmic Functions Exponential Functions: ● Form: y = a(b)^x → a = initial value, b = base (growth/decay rate) Growth: b > 1 Decay: 0 < b < 1 Logarithms: ● log = inverse of exponentials log_b(x) = y means → b^y = x Log Rules: ● log_b(xy) = log_b(x) + log_b(y) ● log_b(x/y) = log_b(x) - log_b(y) ● log_b(x^a) = a * log_b(x) Chapter 9: Sequences & Series Arithmetic Sequence: ● a_n = a₁ + (n - 1)d → Constant difference d Geometric Sequence: ● a_n = a₁ * r^(n - 1) → Constant ratio r Sums: ● Arithmetic: S_n = n/2 * (a₁ + a_n) ● Geometric: S_n = a₁(1 - r^n)/(1 - r) (if |r| ≠ 1) Chapter 10: Probability & Statistics Probability: ● P(event) = favorable outcomes / total outcomes Independent = doesn’t affect other Dependent = affects the next Permutations vs. Combinations: ● Permutation = order matters → nPr = n! / (n - r)! ● Combination = order doesn’t matter → nCr = n! / [r!(n - r)!] Chapter 11: Matrices (kinda fun tbh) Matrix = a box of numbers Add/Subtract → just add corresponding entries Multiply → row × column dot product Example: [1 2] [3] [3 4] × [1] → [1*3 + 2*1] = [5] [3*3 + 4*1] = [13]

Radical Equations and Complex Numbers

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