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.
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.
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.
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.
No, that is not what you do.
To divide by a complex number, write it as a fraction and then multiply the numerator and denominator by the complex conjugate of the denominator - this is formed by changing the sign of the imaginary bit of the number; when a complex number (a + bi) is multiplied by its complex conjugate the result is the real number a² + b² which can be divided into the complex number of the numerator: (-4 - 3i) ÷ (4 + i) = (-4 - 3i)/(4 + i) = ( (-4 - 3i)×(4 - i) ) / ( (4 + i)×(4 - i) ) = (-16 + 4i - 12i + 3i²) / (4² + 1²) = (-16 - 8i - 3) / (16 + 1) = (-19 - 8i)/17
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.
To eliminate the radical in the denominator.
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.
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.
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.
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.
complex
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.
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.
"conjugate" That step is called "rationalizing the denominator", although it actually makes the denominator 'real', but not necessarily 'rational'.
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.
No, that is not what you do.