Closure: The sum of two real numbers is always a real number. Associativity: If a,b ,c are real numbers, then (a+b)+c = a+(b+c) Identity: 0 is the identity element since 0+a=a and a+0=a for any real number a. Inverse: Every real number (a) has an additive inverse (-a) since a + (-a) = 0 Those are the four requirements for a group.
2a + 6b = c, where a, b, and c are all numbers from the domain of your choice. Usually, in algebra, the real number set R is used as the domain. In this case, you would need to select values from R for a and b which will yield the value of c. Since this function is closed in the real number system, c will always be a real number, given that a and b are real numbers.
The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping:(a + b) + c = a + (b + c)
Algebraic Properties of Real Numbers The basic algebraic properties of real numbers a,b and c are: Closure: a + b and ab are real numbers Commutative: a + b = b + a, ab = ba Associative: (a+b) + c = a + (b+c), (ab)c = a(bc) Distributive: (a+b)c = ac+bc Identity: a+0 = 0+a = a Inverse: a + (-a) = 0, a(1/a) = 1 Cancelation: If a+x=a+y, then x=y Zero-factor: a0 = 0a = 0 Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
In (a+bi) + (c+di), you add the real parts using the laws for real numbers and do the same for the imanginary parts. (a+c)+(b+d)i
If you are talking about pure imaginary numbers (a complex number with no real part) then no. Example: bi times ci where b and c are real numbers equals b*c*i² = b*c*(-1) = -b*c, which is a real number, because b & c & -1 are all real numbers. If you're talking about multiplying two complex numbers (a + bi)*(c + di), then the product will be complex, but it could be real or imaginary, depending on the values of a, b, c, & d.
The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping:(a + b) + c = a + (b + c)
ab x ac = ab+c, where a, b, and c are all real numbers.
Closure: The sum of two real numbers is always a real number. Associativity: If a,b ,c are real numbers, then (a+b)+c = a+(b+c) Identity: 0 is the identity element since 0+a=a and a+0=a for any real number a. Inverse: Every real number (a) has an additive inverse (-a) since a + (-a) = 0 Those are the four requirements for a group.
You compare the results for each of the six possibilities: a<b<c, a<c<b, etc.
2a + 6b = c, where a, b, and c are all numbers from the domain of your choice. Usually, in algebra, the real number set R is used as the domain. In this case, you would need to select values from R for a and b which will yield the value of c. Since this function is closed in the real number system, c will always be a real number, given that a and b are real numbers.
The sign of the quotient will be positive. +A/+B = +C. -A/-B = +C. This assumes B is not zero.
ab x ac = ab - ac
a(b + c) = ab + ac where a, b and c are any real numbers.
The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping:(a + b) + c = a + (b + c)
The distributive property states that for any real numbers a, b, and c, the product of a and the sum (or difference) of b and c is equal to the sum (or difference) of the products of a and b and a and c. In mathematical terms, it can be written as a(b + c) = ab + ac or a(b - c) = ab - ac, where a, b, and c are real numbers. This property is fundamental in algebraic operations and simplifying expressions.
Algebraic Properties of Real Numbers The basic algebraic properties of real numbers a,b and c are: Closure: a + b and ab are real numbers Commutative: a + b = b + a, ab = ba Associative: (a+b) + c = a + (b+c), (ab)c = a(bc) Distributive: (a+b)c = ac+bc Identity: a+0 = 0+a = a Inverse: a + (-a) = 0, a(1/a) = 1 Cancelation: If a+x=a+y, then x=y Zero-factor: a0 = 0a = 0 Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab