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Yes, the complex numbers, as well as the real numbers which are a subset of the complex numbers, form groups under addition.

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Q: Do the complex numbers for a group under binary operation ' plus '?
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What is an additive group?

An additive group is an abelian group when it is written using the + symbol for its binary operation.


What is a fraction operation that creates groups of numbers?

if you take a vector (= group of numbers) and you divide it by a scalar (=one number) then you get a vector (=group of numbers)


What are the characteristics of real numbers?

The real number system is a mathematical field.To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility.In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first.And finally, a Field is a Ring over which division - by non-zero numbers - is defined.There are several mathematical terms above which have been left undefined to keep the answer to a manageable size. All these algebraic structures are more than a term's worth of studying. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!


What is the properties of complex numbers when you are considering it in case of group?

The properties of an array or group or complex numbers form a system of real and imanginary numbers that are at a 90 degree angle to each other. Refer to the Related Link and notice that in both panes, the lines are at 90 degrees.


What is axioms of real number?

The real number system is a mathematical field. To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility. In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first. And finally, a Field is a Ring over which division - by non-zero numbers - is defined. The algebraic structures (Group, Ring, Field) are more than a term's worth of studying. There are also several mathematical terms above which have been left undefined to keep the answer to a manageable size. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!

Related questions

What is an additive group?

An additive group is an abelian group when it is written using the + symbol for its binary operation.


What is ring and group in algebra?

Rings and Groups are algebraic structures. A Groupis a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility. In addition, it is a Ring if it is Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first.


What is a fraction operation that creates groups of numbers?

if you take a vector (= group of numbers) and you divide it by a scalar (=one number) then you get a vector (=group of numbers)


Is set of real numbers a group?

The answer depends on the operation under consideration.


Is the set of rational numbers a commutative group under the operation of division?

No, it is not.


Properties of the set of real numbers?

The real number system is a mathematical field. To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility. In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first. And finally, a Field is a Ring over which division - by non-zero numbers - is defined. There are several mathematical terms above which have been left undefined to keep the answer to a manageable size. All these algebraic structures are more than a term's worth of studying. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!


What are the characteristics of real numbers?

The real number system is a mathematical field.To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility.In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first.And finally, a Field is a Ring over which division - by non-zero numbers - is defined.There are several mathematical terms above which have been left undefined to keep the answer to a manageable size. All these algebraic structures are more than a term's worth of studying. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!


What is the properties of complex numbers when you are considering it in case of group?

The properties of an array or group or complex numbers form a system of real and imanginary numbers that are at a 90 degree angle to each other. Refer to the Related Link and notice that in both panes, the lines are at 90 degrees.


What is axioms of real number?

The real number system is a mathematical field. To start with, the Real number system is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element which is also in the set. The Group satisfies four axioms: closure, associativity, identity and invertibility. In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative) and it has a second binary operation (multiplication) that is defined on its elements. This second operation is distributive over the first. And finally, a Field is a Ring over which division - by non-zero numbers - is defined. The algebraic structures (Group, Ring, Field) are more than a term's worth of studying. There are also several mathematical terms above which have been left undefined to keep the answer to a manageable size. You can find out more about them using Wikipedia but be sure to select the hit that has "mathematical" in it!


Pq plus qp?

If you are working with real numbers, or even complex numbers, pq is the same as qp, so the result is the same as 2pq. If you use some multiplication that is NOT commutative (such as, when you multiply matrices), you can't simplify the expression.


Why are the rational numbers under the operation of multiplication not a group?

I believe it is because 0 does not have an inverse element.


What is a group of numbers that most people know?

The decimal, binary, hexadecimal, and roman numeral systems are fairly well known.