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ALGEBRA PROPERTIES, ARITHMETIC PROPERTIES, EXPONENT PROPERTIES, PROPERTIES OF INEQUALITIES, Ifa cb then a+e < b+c and a-e<a-e, Ifa <b and e>0 then ac < be and a/e < b/e, ASSOCIATIVE, a(bc) = (ab)c, a"am = a"+m, COMMUTATIVE a+b=b+a and ab = ba, a(b +c) = ab + ac, (a")m = a™m, If a <b and e< 0 then ac> be and a/e > b/e, DISTRIBUTIVE, (ab)" a"b", PROPERTIES OF COMPLEX NUMBERS, ARITHMETIC OPERATIONS EXAMPLES, ab + ac = a(b +c), a c, ad – be, =-1, bd, ()-, ab, (5)"-(4) --, D = D-A, (a + bi) + (c+ di) a+c+(b+d)t, a-b b-a, c-d, a+b a b, (a + bi) - (c+ di) = a-c+(b-d)i, (a + bi)(c + di) = ac- bd + (ad +bc)t, (a + bi)(a - bi) = a² +b, = am =, bc, ab + ac, =b+c, a=0, a° = 1,a =0, ) ad, (;) -, ad + bc, la + bil = Va+b-, bd, be, (a + b1) = a- bi, (a+ bi)(a + bi) = la+ bil, QUADRATIC EQUATION, 1, (a-bi), a- bi, Forthe equation, -btVb-4ac, (14 – D)(19 + D) _ 69 +0), 2a, ax+ bx +c = 0, COMMON FACTORING EXAMPLES, ABSOLUTE VALUE, RADICAL PROPERTIES, LOGARITHM PROPERTIES, sa, ifa 20, lal =, 1-a, if a<0, x-a = (x +a)(x- a), a,b 20 for even n, ify = log, x then b" = x, x+ 2ax +a = (x +a):, x- 2ax + a = (x- a):, x + (a +b)x +ab = (x+a)(x+b), x + 3ax? + 3ax+ a (x+a), x3 +a? = (x +a)(x* - ax+ a?), x-a= (x-a)(x+ax+ a"), log, b =1 and log, 1= 0, log, b =x, Blog =x, Va, = an, lal = |-al, lal 20, log, x, log x=, log, a, Vab = Vav5, lab = Jal|bl, %3D, lal, log,(x)= rlog, x, log (xy) = log, x+logs y, Va = a,ifn is odd, Va = lal, ifn is even, la + bl s lal + lbl, log. (), = log, x- log, y, x2* -a = (x" - a")(x"+a")