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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).
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Is the sum of any two prime numbers always a composite number?
The sum of any two prime numbers is not always a composite number. The sum of 2 and 11 is 13, and 13 is a prime number, not a composite number.
Which number belongs to the set of complex numbers?
Lots of numbers do. To begin, all real numbers do. Multiples of sqrt(-1), aka. imaginary numbers, do. The Complex Numbers are all numbers which are the sum of a real number and an imaginary number.
The sum of two rational numbers is always a rational number?
Yes.
Is the sum of two whole numbers always a whole number?
Yes.
when adding mixed numbers,is it always necessary to write the sum as a mixed number Explain?
what is 2+@
Is the sum of two odd numbers is always odd?
The sum of two odd numbers is always even.
What happens when you add an odd number and an odd number?
Two odd numbers always sum to an even number. Always. Two even numbers always sum to an even number, and an odd number and an even number always sum to an odd number.
Why is the sum of three odd numbers always odd?
Because the sum of two odd numbers is always even and the sum of that even number plus another odd number is always odd.
The sum of two positive numbers is?
The sum of two positive numbers is always a positive number.
The sum of two even numbers?
The sum of two even numbers is always an even number.
What is the sum of two odd numbers?
The sum of two odd numbers is always an even number
What is the sum of two even numbers?
The sum of two even numbers is always an even number.
Is the sum of any two prime numbers always a composite number?
The sum of any two prime numbers is not always a composite number. The sum of 2 and 11 is 13, and 13 is a prime number, not a composite number.
Five odd numbers whose sum is 20?
That can't be solved. The sum of five odd numbers will always be an odd number.That can't be solved. The sum of five odd numbers will always be an odd number.That can't be solved. The sum of five odd numbers will always be an odd number.That can't be solved. The sum of five odd numbers will always be an odd number.
Which number belongs to the set of complex numbers?
Lots of numbers do. To begin, all real numbers do. Multiples of sqrt(-1), aka. imaginary numbers, do. The Complex Numbers are all numbers which are the sum of a real number and an imaginary number.
What is triangular inequality of complex number?
The absolute value of the sum of two complex numbers is less than or equal to the sum of their absolute values.
Is the sum of two consecutive numbers always divisible by 2?
No, the sum of two consecutive numbers is always an odd number, and is not divisible by two.
