5 6.2 – Simplified Form for Radicals Rationalizing the DenominatorRadical expressions, at times, are easier to work with if the denominator does not contain a radical. The process to clear the denominator of all radicals is referred to as rationalizing the denominator
18 6.4 –Multiplication and Division of Radical Expressions Examples:
19 6.4 –Multiplication and Division of Radical Expressions If the denominator contains a radical and it is not a monomial term, then the use of a conjugate is required in order to rationalize the denominator.conjugate
20 6.4 –Multiplication and Division of Radical Expressions Example:
21 6.4 –Multiplication and Division of Radical Expressions Example:
24 6.5 – Equations Involving Radicals Suggested Guidelines:1) Isolate the radical to one side of the equation.2) Square both sides of the equation.3) Simplify both sides of the equation.4) Solve for the variable.5) Check all solutions in the original equation.
33 6.6 – Complex Numbers Complex Number System: This system of numbers consists of the set of real numbers and the set of imaginary numbers.Imaginary Unit:The imaginary unit is called i, whereandSquare roots of a negative number can be written in terms of i.
34 Operations with Imaginary Numbers 6.6 – Complex NumbersThe imaginary unit is called i, whereandOperations with Imaginary Numbers
35 6.6 – Complex Numbers The imaginary unit is called i, where and Numbers that can written in the form a + bi, where a and b are real numbers.3 + 5i8 – 9i–13 + iThe Sum or Difference of Complex Numbers