Using the extended Euclidean algorithm, find the multiplicative inverse of a) 1234 mod 4321
7
Find the additive inverse (opposite) of: 18/23
The additive inverse of 6+4i is -6-4i since their sum is 0. It is analogous to real numbers where the additive inverse of 6 is -6 since 6+-6 =6-6=0 In the case of complex numbers, we add them by adding the real parts and then adding the imaginary parts. So to find the complex additive inverse of a+bi, we find the inverse of a which is -a and of bi which is -bi and so the additive inverse is -a-bi
To find the sum of two mixed numbers, turn the mixed numbers into improper fractions (multiply the base with the denominator and add the numerator), then add the two fractions. To add the two fractions, find the LCD (lowest common denominator) and add the two numerators, but leave the denominators the same.
Divide 1 by the number. The multiplicative inverse of 7 is 1/7, for example.
Swap the numerator and denominator. For example, the multiplicative inverse of 5/7 is 7/5
Using the extended Euclidean algorithm, find the multiplicative inverse of a) 1234 mod 4321
The multiplicative inverse of a number is its reciprocal, meaning the multiplicative inverse of the rational number a/b is b/a. In the specialized case for integers, the multiplicative inverse of n is 1/n. This is due to the fact that a/b * b/a = 1 and n * 1/n = 1, which is the definition of a multiplicative inverse. More succinctly, to find the multiplicative inverse you "flip" the fraction or integer around to its reciprocal. This is the number that when multiplied with the original number results in a product of 1.
The same number....
The answer depends on what you mean by "opposite": whether it is the additive inverse or the multiplicative inverse.
The answer depends on what you mean by "opposite": whether it is the additive inverse or the multiplicative inverse.
7
9/5
find the inverse of (1,-5)(3,-3)(4,-2)
I guess you mean a mixed fraction, such as 5 2/3, which basically means 5 + 2/3. To get the multiplicative inverse, you must first convert the fraction to an improper fraction (in this example, 17/3). Then, to get the multiplicative inverse, you exchange top and bottom (in this example, 3/17). Note that to do the conversion, I multiplied 5 x 3, and added 2 to the result. This number (17) goes into the numerator (top); the denominator (bottom) doesn't change.
Additive inverse: change all signs. Multiplicative inverse: flip it over.