Update Unit 2: Quadratic Equations.md

Grade 10/Math/MPM2DZ/Unit 2: Quadratic Equations.md

@@ -77,10 +77,29 @@ x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\
 - $`a+bi`$ and $`a-bi`$ are conjugates(same term with opposite signs).
 - Complex roots of a quadratic quation occurs in **conjugate pairs**, recall discriminant, if its less than 0, there are 2 complex roots that are **conjugates** ($`a \pm bi`$)
 
+|Complex Number|Equivalent|
+|:--------------|:---------|
+|$`i`$|$`\sqrt{-1}`$|
+|$`i^2`$|$`-1`$|
+|$`i^3`$|$`-\sqrt{-1}`$ or $`-i`$|
+|$`i^4`$|$`1`$|
+
 ## Number Systems
 
 <img src="https://www.shelovesmath.com/wp-content/uploads/2018/10/Venn-Diagram-of-Numbers.png" width="500">
 
+- **Natural Numbers** $`\mathbb{N} = \{1,2,3, \cdots\}`$
+- **Whole Numbers** $`\mathbb{W} = \{0, 1, 2, 3\cdots\}`$
+- **Integers** $`(\mathbb{I}`$ or $`\mathbb{Z}) = \{\cdots, -2, -1, 0,1,2, \cdots\}`$
+- **Rational numbers** $`(\mathbb{Q}) = \{\frac{a}{b}, a, b, \in \mathbb{I}, b =\not 0\}`$
+- **Irrational Numbers** $`(\mathbb{Q} \prime)`$: any real number that cannot be written as $`\frac{a}{b}, a, b, \in \mathbb{I}, b =\not 0`$
+- **Real Numbers** $`(\mathbb{R})`$: the set of $`\mathbb{Q} \cup \mathbb{Q} \prime`$
+- **Complex Numbers** $`\mathbb{C}`$: any number that can be expressed in the form $`a+ib`$ (includes the set of real numbers) 
 
 
-
+## Radical Equations
+- `Extraneous Sol` $`\rightarrow`$ $`LS =\not RS`$
+- `Inadmissable Sol` $`\rightarrow`$ Solutions you reject due to problem statement, eg negative length.
+- `Extraneous values` occur because squaring both sides of an equation is not a reversible step.
+- Make sure to check your work after working with radical equations, since squaring both sides is not a reversible step. Thus equations must be verified by pluging it back into the equation.
+- **Radical Equations** are called that because the variable occurs under a radical sign. We **rationalize** the radical variable before continuing to slve the equation.