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An imaginary number is a number, which when squared, gives a negative real number. Any positive or negative real number, when squared, will give a positive real number. Imaginary numbers were originally conceived (around the 1500's) to provide solutions to equations which required there be a solution to the square root of a negative real number. Originally, that was the only purpose that they served, so they were given the term imaginary. The imaginary numbers were shown to be graphically at a 90° angle to real numbers. Complex numbers are the combination of real and imaginary numbers, and can be plotted graphically on a complex plane, just like you would plot x and y coordinates on a regular 2-dimensional plane.
Through the work of Euler in the 1700's and others, a relationship between imaginary numbers and the behavior of waves and oscillating motion was worked out. See related link for some interesting information about imaginary and complex numbers.
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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 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.
Can a complex number be imaginary?
Yes, imaginary numbers are a subset of complex numbers.
Can a number be both complex and imaginary?
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
Is all complex numbers imaginary?
No.
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.
Why are complex numbers imaginary?
An imaginary number has the form b*i, where b is any real number, and i is the imaginary unit number sqrt(-1). A complex number is in the form a + b*i, where a and b are any real number. Complex numbers are called complex, because they combine numbers from the real domain and the imaginary domain.I thought the Wikipedia article was very good. Also, Answers.com has a video about complex and imaginary numbers.
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.
How are complex numbers and real numbers related?
Complex numbers extend the concept of real numbers by introducing an imaginary unit, denoted as "i." Real numbers can be considered a subset of complex numbers with the imaginary part equal to zero. Complex numbers include both a real and imaginary component, allowing for operations like addition, subtraction, multiplication, and division.
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.
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 are pure imaginary numbers?
complex numbers with no real partif any complex number z can be written a + i bthen pure imaginary numbers have a=0 and b not equal to 0
