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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).
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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.
Can a complex number be imaginary?
Yes, imaginary numbers are a subset of complex numbers.
What is the difference between imaginary numbers and complex numbers?
No difference. The set of complex numbers includes the set of imaginary 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.
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.
