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If you are talking about pure imaginary numbers (a complex number with no real part) then no. Example: bi times ci where b and c are real numbers equals b*c*i² = b*c*(-1) = -b*c, which is a real number, because b & c & -1 are all real numbers. If you're talking about multiplying two complex numbers (a + bi)*(c + di), then the product will be complex, but it could be real or imaginary, depending on the values of a, b, c, & d.
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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.
When is product of 2 prime numbers a prime number?
The product of two prime numbers is always a composite number, and it never is a prime number.
Is the product of 33 negative numbers and 3 positive numbers a positive or negative number?
The product of all those numbers will always be a negative 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.
Is Every complex number is a pure imaginary number?
No. All Complex Numbers are of the form a + bi where a and b are Real Numbers and i is the square root of -1. So only ones where a = 0 are pure Imaginary Numbers.
Is the product of two imaginary numbers always a pure imaginary number?
no
Is the product of two pure imaginary numbers a real number?
Yes it is.
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 product of two numbers with different signs is always a negative?
The product of negative number and a positive number is always a negative. The product of two positive numbers, or two negative numbers, is always a positive.
Is the product of two rational numbers irrational?
The product of two rational numbers is always a rational number.
Is the product of two negative numbers always a real negative number?
No, the product of two negative numbers is always a positive.
What is the product of two odd numbers?
The product of two odd numbers is always an odd number.
What is an unreal number?
Imaginary and complex numbers are an extension of the Real Number system. They are not called unreal. An imaginary number is a non-existent number, like the square root of a negative number. For example, the square root of -4 is 2i (i stands for imaginary). There are also complex numbers, which are defined as the sum of a real number and an imaginary number (e.g. 4 + 3i). An imaginary number does not exist, but can nevertheless be useful in certain applications. An imaginary number is any number that is the product of a real number and the square root of negative one (-1). The square root of -1 is the "unit" of the set of imaginary numbers, and is referred to as "i". As you know, negative numbers cannot have square roots, and so the square root of any negative number is "imaginary". There are also "complex numbers", which are the sum of a real number and an imaginary number. For example 3 + 2i.
When you multiply any number of even numbers will the product always be odd?
No, the product will always be even.
How do you know that the product of any two numbers greater than i must be a composite number?
Prime numbers have only two factors: one and themselves. By definition, your product would have more than that: one, the product and at least the two numbers that created the product. It has to be composite.
What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary numbers.
When is product of 2 prime numbers a prime number?
The product of two prime numbers is always a composite number, and it never is a prime number.
