0
What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
Wiki User
∙ 14y ago
To eliminate the radical in the denominator.
Wiki User
∙ 14y ago
Add your answer:
Earn +20 pts
How do you rationalize a denominator?
You multiply the numerator and the denominator by the same expression - and do it in such a way that the denominator becomes rational.Example 1: The denominator is square root of 5, which I will call root(5). If you multiply top and bottom by root(5), the denominator will become rational. Example 2: The denominator is root(2) + root(3). If you multiply top and bottom by root(2) - root(3), then the denominator will become rational.
Can you use conjugates to rationalize the denominator even when the denominator contains two radical terms?
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.
What is the conjugate of 100?
"Conjugate" usually means that in one of two parts, the sign is changed - as in a complex conjugate. If the second part is missing, the conjugate is the same as the original number - in this case, 100.
To rationalize a denominator that has more than one term you multiply the fraction by where B is the conjugate of the denominator.?
Yes, that is correct.
What is conjugate of 2 3i 2-5i?
The conjugate of 2 + 3i is 2 - 3i, and the conjugate of 2 - 5i is 2 + 5i.
When dividing complex numbers the first step is to multiply the top and bottom by the complex ----- of the denominator?
"conjugate" That step is called "rationalizing the denominator", although it actually makes the denominator 'real', but not necessarily 'rational'.
How do you convert the complex number to standard form 1 plus 2i over root2 plus i?
Multiply the numerator and denominator by the complex conjugate of the denominator ... [ root(2) minus i ]. This process is called 'rationalizing the denominator'.
Which operation involves complex numbers requires the use of a conjugate to be carried out?
One operation that is used a lot in quantum mechanics is taking the absolute value of the square of a complex number. This is equivalent to multiplying the complex number by its complex conjugate - and doing this is simpler in practice.
How do you rationalize the denominator of a radical expression that has two terms in the denominator?
You multiply the numerator and the denominator by the "conjugate" of the denominator. For example, if the denominator is root(2) + root(3), you multiply top and bottom by root(2) - root(3). This will eliminate the roots in the denonimator.
How do you rationalise the denominator?
It depends on what the denominator was to start with: a surd or irrational or a complex number. You need to find the conjugate and multiply the numerator by this conjugate as well as the denominator by the conjugate. Since multiplication is by [conjugate over conjugate], which equals 1, the value is not affected. If a and b are rational numbers, then conjugate of sqrt(b) = sqrt(b) conjugate of a + sqrt(b) = a - sqrt(b), and conjugate of a + ib = a - ib where i is the imaginary square root of -1.
When simplifying radical expressions by rationalizing the denominator what is meant by finding the conjugate of the denominator?
The 6th radical is raising something to the 1/6 power, and the 5th radical is the 1/5 power. Dividing means you subtract the exponents, and 1/6-1/5 is -1/30. The answer would be 1/(30th rad of the term).
What is the first step when dividing complex numbers?
The first step when dividing complex numbers is to find the conjugate of the denominator, which is the same expression but with the sign of the imaginary part changed. This is done to eliminate the imaginary part in the denominator.
How do you rationalize a denominator?
You multiply the numerator and the denominator by the same expression - and do it in such a way that the denominator becomes rational.Example 1: The denominator is square root of 5, which I will call root(5). If you multiply top and bottom by root(5), the denominator will become rational. Example 2: The denominator is root(2) + root(3). If you multiply top and bottom by root(2) - root(3), then the denominator will become rational.
How do you simplify complexed fractions?
You multiply the numerator and the denominator of the complex fraction by the complex conjugate of the denominator.The complex conjugate of a + bi is a - bi.
How do you simplify a complex fraction?
You multiply the numerator and the denominator of the complex fraction by the complex conjugate of the denominator.The complex conjugate of a + bi is a - bi.
What's first step is to multiply top and bottom of the conjugate of the denominator?
Either: when given a fraction with a surd as the denominator, rationalising the denominator; Or, when given a fraction with a complex denominator, to make the denominator real.
What is the conjugate of a denominator?
This is related to the technique used to eliminate square roots from the denominator. If, for example, the denominator is 4 + root(3), you multiply both numerator and denominator by 4 - root(3). In this case, "4 - root(3)" is said to be the "conjugate" of "4 + root(3)". When doing this, there will be no more square roots in the denominator - but of course, you'll instead have a square root in the numerator.
