Complex Numbers Addition and Subtraction The complex numbers follow the commutative and associative laws of addition. Thus we can add and subtract them as we do binomials with real-number coefficients…
Month: May 2014
The Complex Numbers Imaginary and Complex Numbers
The Complex Numbers Imaginary and Complex Numbers Negative numbers do not have square roots in the real-number system. However, mathematicians have described a larger number system that contains the…
Equations with Two Radical Terms
Equations with Two Radical Terms A general strategy for solving radical equations, including those with two radical terms, is as follows. SOLVING RADICAL EQUATIONS To solve radical equations: a.…
Solving Radical Equations
SOLVING RADICAL EQUATIONS The Principle of Powers A radical equation has variables in one or more radicands—for example, + 1 = 5, + = 7. To solve such an equation,…
More in Division of Radical Expressions
MORE ON DIVISION OF RADICAL EXPRESSIONS Rationalizing Denominators Sometimes in mathematics it is useful to find an equivalent expression without a radical in the denominator. This provides a standard notation…
Addition Subtraction and more Multiplication
Addition Subtraction and more Multiplication Addition and Subtraction Any two real numbers can be added. For example, the sum of 7 and can be expressed as 7 + . We…
Dividing and Simplifying Radical Expressions
Dividing and Simplifying Radical Expressions Note that = and that = . This example suggests the following. The Quotient Rule For Radicals For any nonnegative number a, any positive number…
Multiplying and Simplifying Radical Expressions
Multiplying and Simplifying Radical Expressions Note that = 2. 5 – 10. Also = = 10.Likewise, = 3.2 = 6 and = 6. SIMPLIFYING kth ROOTS To simplify a…
Simplifying Radical Expressions
Simplifying Radical Expressions Rational exponents can be used to simplify some radical expressions. The procedure is as follows. SIMPLIFYING RADICAL EXPRESSIONS a. Convert radical expressions to exponential expressions. b. Use…
Laws of Exponents
Laws of Exponents The same laws hold for rational-number exponents as for integer exponents. We list them for review. For any real number a and any rational exponents m…
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