Complex Numbers REAL NUMBERS {x | x is a rational or an irrational number} Imaginary Numbers Irrational Numbers ,  8, -  13 Rational Numbers 1/2 –7/11,

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Presentation transcript:

Complex Numbers REAL NUMBERS {x | x is a rational or an irrational number} Imaginary Numbers Irrational Numbers ,  8, -  13 Rational Numbers 1/2 –7/11, 7/9,.33  9, {p/q | p & q are integers, q  0} Integers {…-2, -1, 0, 1, 2, 3…} Whole Numbers {0,1,2,3,4…} Natural Numbers {1,2,3,4…}

Operations on Real Numbers Addition/Subtraction = = 2-3 – 5 = -8 [ THINK MONEY] 6 – 2 – – 10 = -1 Multplication/Division 3 5 = = (-5) = 152 Like Signs (+ answer) = = Unlike Signs (- answer) 6/3 = 2 6/(-3) = -2(-6)/(-3) = 2 Absolute Value | 4 | = 4|-4| = 4 [ALWAYS POSITIVE] -|4 | = -4 - |-4| = -4 -(-|-4|) = 4 [AFFECTS INSIDE ONLY!!] ** Be sure you can perform all operations with fractions too!

Properties of Real Numbers Commutatative Property Addition: a + b = b + a = x + 5 = 5 + 3x Multiplication: ab = ba(7)(10) = (10)(7) (4a)(5x+8) = (5x+8)(4a) Associative Property Addition: (a + b) + c = a + (b + c)3 + (8 + x) = (3 + 8) + x Multiplication: (a b) c = a (b c) -2 (3x) = (-2 3) x = -6x Distributive Property a(b + c) = ab + ac 5 (x + 2) = 5x + (5)(2) = 5x + 10 a(b – c) = ab - ac 5 (x – 2) = 5x + (5)(-2) = 5x – 10 5x + 4x = (5 + 4)x = 9x Identity Property a + 0 = a0 + a = a5 + 0 = 57x + 0 = 7x a 1 = a1 a = a13x 1 = 13x Inverse Property (Additive Inverse & Multiplicative Inverse) a + (-a) = 0(-a) + a = 03x + (-3x) = 3x – 3x = 0 a (1/a) = 1(1/a) a = 1(1/7) 7 = 1 Multiplication Property of Zero : a 0 = 0 0 a = 0

Introductory Exponents 8 2 =8 8 = = = = - 25 (-5) 2 = 25 Exponents of 1Zero Exponents Anything to the 1 power is itself Anything to the zero power = = 5 x 1 = x (xy) 1 = xy5 0 = 1 x 0 = 1 (xy) 0 = 1 Careful with Negatives! Square Roots  25 = 5 since 5 2 = 25-  25 = -5  -25 is not a real number

Order of Operations Groupings Exponents Multiplication & Division from Left to Right Addition & Subtraction from Left to Right

Calculator Skills for Chapter 1 1.Add, Subtract, Multiply, Divide 2.Exponents/Powers 3.Square Root 4.Absolute Value [Math][Num][Abs] 5.Negative Button – Try | -5|