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1 if the equation has any fractions employ the least common denominator to apparent the fractions we will do this through multiplying both sides of
to solve out linear equations we will make heavy use of the following facts1 if a b then a c b c for any c all it is saying that we can add
linear equationswell begin the solving portion of this chapter by solving linear equationsstandard form of a linear equationa linear equation is any
there is one final topic that we need to address as far as solution sets go before leaving this section consider the following equation and
for inequalities we contain a similar notation based on the complexity of the inequality the solution set might be a single number or it might be
the complete set of all solutions is called as the solution set for the equation or inequality there is also some formal notation for solution
first a solution to an equation or inequality is any number that while plugged into the equationinequality will satisfy the equationinequality thus
multiply the given below and write the answer in standard form2 - radic-100 1 radic-36 solutionif we have to multiply this out in its present form
division of complex numbernow we gave this formula a long with the comment that it will be convenient while it came to dividing complex numbers so
multiply following and write the answers in standard form a 7i -5 2i b 1 - 5i -9 2i solutiona thus all that we have to do is distribute
multiplication of complex numbersafter that lets take a look at multiplication again along with one small difference its possibly easiest to just
performs the mentioned operation and write the answers in standard form -4 7i 5 -10i solutionactually there isnt much to do here other than add or
now we have to discuss the basic operations for complex numbers well begin with addition amp subtraction the simplest way to think of adding andor
the conjugate of the complex number a bi is the complex number a - bi in other terms it is the original complex number along the sign on the
it is totally possible that a or b could be zero and thus in 16i the real part is zero while the real part is zero we frequently will call the
following are some examples of complex numbers3
standard form of a complex numberso lets start out with some of the basic definitions amp terminology for complex numbers the standard form of a
perform the denoted operation 46x2-13x552x3solutionfor this problem there are
lets recall how do to do this with a rapid number
now come to addition and subtraction of rational expressions following are the general formulas ac bc a
reduce the following rational expression to lowest
x4 - 25there is no greatest common factor here though notice that it is the difference of two perfect squaresx4 - 25 x2 2 - 52thus we can
factoring polynomials with degree greater than 2there is no one method for doing these generally however there are some that we can do solets
factor following x2 - 20 x 100solutionin this case weve got three terms amp
special formsthere are a number of nice special forms of some polynomials which can make factoring easier for us on occasion following are the