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The answer is Yes, for the purposes of most Math students. There are, number systems that have been devised which are outside the set of Complex Numbers, though.
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What is the domain of y equals sin x?
All real numbers. Or all complex numbers, if you are working with complex numbers.
Every integer is a complex number?
Yes. Every integer is a rational number. Every rational number is a real number. Every real number is a complex number. The complex numbers include all real numbers and all real numbers multiplied by the imaginary number i=sqrt(-1) and all the sums of these.
Why is the solution to an identity all real numbers?
That is how an identity is defined. If the solution was not true for all numbers, then it would not be called an identity. In fact, it should be true for all complex numbers as well.
What numbers have an absolute value of 8?
8, and minus 8. If you want to include complex numbers, all numbers on a circle with radius 8.
Can The domain of all polynomials are all real numbers?
Yes, it cannot contain any imaginary numbers
What is the domain of y equals sin x?
All real numbers. Or all complex numbers, if you are working with complex numbers.
Which of these are complex numbers 5 3i 1 2i?
All of them. Real numbers are a subset of complex numbers.
Are all rational numbers plus all irrational numbers complex numbers?
no its real numbers
Is -7 a complex number?
Yes, all real numbers are complex numbers.
Is zero a complex number?
Yes. All Real numbers are a proper subset of the Complex numbers.
Is all complex numbers imaginary?
No.
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.
How are real numbers imaginary numbers and complex numbers related?
It helps to visualize the numbers on a plane. The complex numbers occupy the entire plane. The real numbers are all the numbers on the horizontal axis, the imaginary numbers are all the numbers on the vertical axis. A complex number thus has a real and an imaginary part, a + bi, where a and be are real numbers (for example, 3 - 2i).
What is the Multiplicative Identity for rational numbers?
It is 1, as it is for all complex numbers - which includes real numbers.
Is 3 a complex number?
Yes. All real numbers are considered complex numbers, with the imaginary part being equal to zero.
What is the set c?
It is the set of all complex numbers.
What is the cardinality of the set of all complex numbers?
It is the continuum.
