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Real numbers are a proper subset of complex numbers. In fact each complex number, z, can be represented as z = x +iy where x and y are real numbers and i is the imaginary square root of -1.
Thus the set of complex numbers is the Cartesian product of two sets of real numbers. That is, C = R x R where C is the set of complex numbers and R is the set of real numbers. Limitations of this browser prevent me from writing that in a mathematically precise and more helpful fashion.
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What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary numbers.
What is the difference between a complex number and real number system?
Graphically the difference is quite clear: the real numbers can be put on a line, the so-called number-line; while complex numbers are represented as points on a plane. A complex number is made up of two parts, like a vector in two dimensions.
What is the relation of complex numbers to real numbers?
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
Is the difference between two real numbers a real number?
Yes, I can't think of any way that a real number minus another real number would be complex or purely imaginary. My answer is yes.
What is the differrent of imaginary numbers to complex numbers?
Imaginary number is a number that consist of only Imaginary part. Such as i, 40i, 1/2i, etc. While the difference between the imaginary numbers and the complex numbers are that complex number also contains Real numbers, and can be written as a + bi. For example, 30+i, 1/2+1/2i, etc.
What is the difference between a set of real numbers and a set of complex numbers?
The set of real numbers is a subset of the set of complex numbers. For the set of complex numbers, given in the form (a + bi), where a and b can be any real number, the number is only a real number, if b = 0.
What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary numbers.
The difference of two complex numbers is always a complex number?
A complex number is any number that is in the real/imaginary plane; this includes pure reals and pure imaginaries. The difference between two numbers inside this plane is never outside this plane; therefore, yes, the difference between two complex numbers is always a complex number. However, the difference between two numbers that are neither purely imaginary nor purely real is not always necessarily a number that is neither purely imaginary nor purely real. Take x+yi and z+yi for instance, where x, y, and z are all real: (x+yi)-(z+yi)=x+yi-z-yi=x-z. Since x and z are both real numbers, x-z is a real number.
What is the difference between a complex number and real number system?
Graphically the difference is quite clear: the real numbers can be put on a line, the so-called number-line; while complex numbers are represented as points on a plane. A complex number is made up of two parts, like a vector in two dimensions.
What is the difference between a complex number and a non real complex number?
Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.Think of the complex numbers as points on a coordinate system. Instead of the usual x-axis you have the real numbers, instead of the y-axis, you have the imaginary numbers.The real numbers are on the horizontal axis.The imaginary numbers are on the vertical axis.The complex numbers are any number on the plane.The non-real complex are, of course, any complex numbers that are not on the real number axis - not on the horizontal axis.
What is the relation of complex numbers to real numbers?
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
Is the difference between two real numbers a real number?
Yes, I can't think of any way that a real number minus another real number would be complex or purely imaginary. My answer is yes.
What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What is the differrent of imaginary numbers to complex numbers?
Imaginary number is a number that consist of only Imaginary part. Such as i, 40i, 1/2i, etc. While the difference between the imaginary numbers and the complex numbers are that complex number also contains Real numbers, and can be written as a + bi. For example, 30+i, 1/2+1/2i, etc.
What is the Difference between an integer and a real number?
Integer numbers are a subset of real numbers. Real numbers may contain fractions.
How is solving a quadratic equation with complex numbers like solving a quadratic equation with real numbers?
Because of how close the two are. The only difference between the two is that a complex number is any whole number along side of a fraction, while a real number is any positive number.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
