Algebra Chapter 7 Test: Radicals
adding/subtracting complex numbers
add/subtract the real parts; add/subtract the imaginary parts (essentially just combine the like terms)
complex number
any number that can be written in the standard form a + bi, where "a" and "b" are real numbers, and i=√(-1)
how to rationalize the denominator
multiply by the conjugate or by the smallest radical to effectively cancel out any radicals in the denominator
radicand
the number under a radical symbol
multiplying/dividing complex numbers
treat "i" as a variable and distribute appropriately (see image for example)
(x/y)²
x²/y²
(xy)²
x²y²
x²x³
x⁵
(x²)³
x⁶
(x/y)⁻²
y²/x²
graphing complex numbers
|a+bi| → (a, b) ex: |-3+5i| → (-3, 5) use the pythagorean thm to calculate the distance of this graphed point from the origin
√¼
½
i¹
√(-1)
x⁰
1
i⁴
1 (use this property to simplify!!)
x²/x³
1/x
x⁻²
1/x²
³√1000
10
√100
10
√111
11
√144
12
√169
13
√196
14
√225
15
√256
16
√289
17
√324
18
√361
19
³√8
2
⁴√16
2
⁵√32
2
⁶√64
2
√4
2
√400
20
³√27
3
⁴√81
3
⁵√243
3
⁶√729
3
√9
3
³√64
4
⁴√256
4
⁵√1024
4
√16
4
³√125
5
⁴√625
5
⁵√3125
5
√25
5
³√216
6
⁴√1296
6
√36
6
³√343
7
√49
7
³√512
8
√64
8
³√729
9
√81
9
i²
-1
i³
-i
