# Combine like terms replace 2iwith 1 simplify simplify

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Distribute/FOIL. Combine like terms.Replace 2iwith (-1). Simplify. Simplify4.) (3 + 7i) (8 2i) 5.) (2 + 5i) + (7 2i)6.) (2 + i)(5 + 2i)7.) (3 i)(5 2i)B. Dividing complex numbersIf i is part of a monomialon the denominator, multiply top and bottom byi.ex: 56iIf i is part of a binomialon the denominator, multiply top and bottom by the complex conjugate of the denominator (same expression but opposite sign). FOIL. ex: 56iReplace 2iwith (-1). Simplify. 8.) 34i9.) 642ii10.) 27ii11.) 7514ii12
Section 4.7: Completing the SquareB. Review: Solving Using Square RootsFactor and write one side of the equation as the square of a binomialSquare root both sides of the equation (include + and – on the right side; 2 equations!Solve for the variable (make sure there are no roots in the denominator)1) (k + 2)2= 122.) x2+ 2x+ 1 = 83.) n2– 14n+ 49 = 3C. Completing the Square20axbxcTake half the b(the xcoefficient)Square this number (no decimals – leave as a fraction!)Add this number to the expressionFactor – it should be a binomial, squared ( )24.) x2+ 6x+ _____5.) m2– 14m+ _______( )( )( )2Find the value of c such that each expression is a perfect square trinomial. Then write the expression asthe square of a binomial.6.) w2+ 7w+ c7.) k2– 5k+ cSolving by Completing the Square:Collect variables on the left, numbers on the rightDivide ALL terms by a; leave as fractions (no decimals!)Complete the square on the left – add this number to BOTH sidesSquare root both sides (include a ______ and _______ equation!)Solve for the variable (simplify all roots – look for 1i)8.) x2+ 4x– 5 = 09.) m2– 5m+ 11 = 1013
Notes #19: Sec. 4-8 Use the Quadratic Formula and the DiscriminantA. Review of Simplifying Radicals and FractionsSimplify expression under the radical sign (1i); reduceReduce only from ALL terms of the fraction. (You can’t reduce a number outside of a radical with a number inside of a radical)Make sure that you have TWO answersSimplify:1.) 61822.) 5202 3.) 42044.) 8272 5.) 29( 5)(5)(2)(3)46.) 29(6)4( 3)( 3)4B. Solving Quadratics using the Quadratic FormulaSo far, we have solved quadratics by: (1) _______________, (2) ______________, and(3) ___________________.The final method for solving quadratics is to use the quadratic formula.Solving using the quadratic formula:Put into standard form (ax2+ bx + c = 0)List a = , b = , c =Plug a, b, and c into 242bbacxaSimplify all roots (look for 1i); reduce15
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