We all know by now that algebra is system of numbers and variables that are represented by letters.These numbers and variables are used to express and solve mathematical equations. Once when you understand basic concepts of math, you will be able to do elementary algebra problems without difficulties. Solving elementary algebra problems – Look at […]

## Complex Numbers Formulas

Definitions A complex number is written as a + bi where a and b are real numbers an i, called the imaginary unit, has the property that i2 = -1. The complex numbers a + bi and a – bi are called complex conjugate of each other. Formulas 1) Equality of complex numbers a + […]

## Exponential Formulas

\( a^p = \underbrace{a \cdot a \cdot \dots a }_p ~~~( \text{if} ~~ p \in \mathbb{N} ) \) \( a^0 = 1 ~~~ (\text{if} ~~~ a \ne 0) \) \( a^r \cdot a^s = a^{r+s} \) \( \frac{a^r}{a^s} = a^{r-s} \) \( \left( a^r\right)^s = a^{r \cdot s} \) \( (a \cdot b)^r = […]

## How to Use Algebra Tiles to Teach Basic Algebra

We can make algebra more efficiently if we use algebra tiles. Algebra tiles are square and rectangular tiles that visually represent parts of algebraic equation. They make learning of algebra much easier and much faster, and students like it. Things you’ll need Algebra tiles– Positive:18 unit tiles and 12 “x” tiles Negative:18 unit tiles and […]

## Solutions of Algebraic Equations

Quadric Equation: \( ax^2 + bx + c = 0 \) Solutions (roots): \( x_{1,2} = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \) If \( D = b^2 – 4ac \) is the discriminant , then the roots are 1. real and unique if D>0 2. real and equal if D=0 3. complex conjugate if D<0 Cubic Equation: \( x^3 + a_1x^2 + a_2x […]