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When simplifying radical expressions by rationalizing the denominator what is meant by finding the conjugate of the denominator?
Wiki User
∙ 11y ago
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).
Wiki User
∙ 11y ago
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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.
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.
Why do you multiply by the complex conjugate?
Whenever a complex number (a + bi) is multiplied by it's conjugate (a - bi), the result is a real number: (a + bi)* (a - bi) = a2 - abi + abi - (bi)2 = a2 - b2i2 = a2 - b2(-1) = a2 + b2 This is useful when dividing complex numbers, because the numerator and denominator can both be multiplied by the denominator's conjugate, to give an equivalent fraction with a real-number denominator.
What does it mean to rationalize a denominator?
Sometimes the denominator is an irrational or complex number (depending on the level that you are at). Rationalising the denominator requires to multiply both the numerator and denominator of the fraction by a suitable number - usually the conjugate - so that when simplified, the denominator is rational - normally an integer.
To rationalize a denominator that has more than one term you multiply the fraction by bb where B is the conjugate of the numerator?
No, that is not what you do.
What is the importance of the conjugate in rationalizing the denominator of a rational expression that has a radical expression in the denominator?
To eliminate the radical in the denominator.
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 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.
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 a simplifie?
Simplify (not simplifie) has many meanings which depend on the context. In the context of ratios or fractions, it means reducing the ratio to its lowest or simplest form. This requires the numerator and denominator to be divided by their greatest common factor. If the fractions contain surds or complex numbers in the denominator, simplifying means removing these to the numerator. This requires multiplying both the numerator and denominator by the conjugate number. In the context of an equation or expression, it means to combine like terms.
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.
Why do you multiply by the complex conjugate?
Whenever a complex number (a + bi) is multiplied by it's conjugate (a - bi), the result is a real number: (a + bi)* (a - bi) = a2 - abi + abi - (bi)2 = a2 - b2i2 = a2 - b2(-1) = a2 + b2 This is useful when dividing complex numbers, because the numerator and denominator can both be multiplied by the denominator's conjugate, to give an equivalent fraction with a real-number denominator.
When dividing complex numbers the first step is to multiply top and bottom by the conjugate of the denominator?
complex
