4.5+&4.6

= 10 9 8 7 6 5 4 3 2 1 BLAST OFF!!! =

Vocabulary 4.5
**Square Root**- a number that produces a specified quantity when multiplied by itself

**Radical**- of or going to the root or origin

**Radicand**- the number or expression beneath a radical sign

**Rationalizing the Denominator**- the process of eliminating a radical expression in the denominator of a fraction by multiplying both the numerator and denominator by an appropriate radical expression

** __Example:__ **
Solvex2 – 4 = 0.

Previously, I'd solved this by factoring the difference of squares, and solving each factor; the solution was "x = ± 2". However—

I can also try isolating the squared variable term, putting the number over on the other side, like this:

x2 – 4 = 0

x2 = 4

I know that, when solving an equation, I can do whatever I like to that equation as long as I do the same thing to both sides of the equation. On the left-hand side of this particular equation, I have an x2, and I need a plain x. To turn an x2 into an x, I can take the square root of each side of the equation:

x = ± 2

Then the solution is x = ± 2

Why did I need the "±" ("plus-minus") sign on the 2 when I took the square root of the 4? Because it might have been a positive 2 or a negative 2 that was squared to get that 4 in the original equation.

Vocabulary 4.6
**Imaginary Unit i**- The square root of -1, corresponding to the point (0,1) in the geometric representation of complex numbers as points in a plane.

**Complex Number**- a number of the form a+bi where a and b are real numbers and i is the square root of -1

Imaginary Number- any complex number of the form i b, where i = √--1

**Complex Conjugates**- the complex number whose imaginary part is the negative of that of a given complex number, the real parts of both numbers being equal: a--ibisthecomplexconjugateofa+ ib

**Complex Plane**- a plane the points of which are complex numbers.

For an explanation of solving quadratic equations by finding square roots:
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