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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.

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โˆ™ 2010-02-07 23:17:06
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Q: The difference of two complex numbers is always a complex number?
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Is an imaginary number always sometimes or never a complex number?

Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.


The sum of two complex numbers is always a complex number?

A "complex number" is a number of the form a+bi, where a and b are both real numbers and i is the principal square root of -1. Since b can be equal to 0, you see that the real numbers are a subset of the complex numbers. Similarly, since a can be zero, the imaginary numbers are a subset of the complex numbers. So let's take two complex numbers: a+bi and c+di (where a, b, c, and d are real). We add them together and we get: (a+c) + (b+d)i The sum of two real numbers is always real, so a+c is a real number and b+d is a real number, so the sum of two complex numbers is a complex number. What you may really be wondering is whether the sum of two non-real complex numbers can ever be a real number. The answer is yes: (3+2i) + (5-2i) = 8. In fact, the complex numbers form an algebraic field. The sum, difference, product, and quotient of any two complex numbers (except division by 0) is a complex number (keeping in mind the special case that both real and imaginary numbers are a subset of the complex numbers).


The difference of two natural numbers is always a natural number?

No. The difference can be a negative integer which is not a natural number.


Is -7 a complex number?

Yes, all real numbers are complex numbers.


The difference of two rational numbers is always a rational number?

Yes, that's true.

Related questions

What is the difference between imaginary numbers and complex numbers?

No difference. The set of complex numbers includes the set of imaginary numbers.


Is the difference of 2 whole numbers always a whole number?

Yes, the difference of two whole numbers is always a whole number.


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.


Is an imaginary number always sometimes or never a complex number?

Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.


The sum of two complex numbers is always a complex number?

A "complex number" is a number of the form a+bi, where a and b are both real numbers and i is the principal square root of -1. Since b can be equal to 0, you see that the real numbers are a subset of the complex numbers. Similarly, since a can be zero, the imaginary numbers are a subset of the complex numbers. So let's take two complex numbers: a+bi and c+di (where a, b, c, and d are real). We add them together and we get: (a+c) + (b+d)i The sum of two real numbers is always real, so a+c is a real number and b+d is a real number, so the sum of two complex numbers is a complex number. What you may really be wondering is whether the sum of two non-real complex numbers can ever be a real number. The answer is yes: (3+2i) + (5-2i) = 8. In fact, the complex numbers form an algebraic field. The sum, difference, product, and quotient of any two complex numbers (except division by 0) is a complex number (keeping in mind the special case that both real and imaginary numbers are a subset of the complex numbers).


Is the difference of two numbers always an even number?

No, it is not always so.


The difference of two even number is always an even number?

Yes, the difference between two even numbers is always an even number.


Is The difference of two real numbers always an irrational number?

No. 5 and 2 are real numbers. Their difference, 3, is a rational 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.


The difference of two natural numbers is always a natural number?

No. The difference can be a negative integer which is not a natural number.


Are the difference of two even numbers always an even number?

Yes.


Is the difference of two natural numbers always a rational number?

Yes, it is.

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