Lonewolf said:
Complex numbers are a type of number that consists of a real part and an imaginary part. The imaginary part is represented by the letter "i" and is defined as the square root of -1. Complex numbers are written in the form a + bi, where a is the real part and bi is the imaginary part.
Quaternions are a type of number that extends the concept of complex numbers by adding two additional imaginary units, j and k. They are written in the form a + bi + cj + dk, where a, b, c, and d are real numbers.
Octonions are a type of number that extends the concept of quaternions by adding six additional imaginary units. They are written in the form a + bi + cj + dk + el + fm + gn + ho, where a, b, c, d, e, f, g, and h are real numbers.
Quaternions and octonions are used in many areas of science, such as physics, engineering, and computer graphics. They are particularly useful for representing rotations and orientations in three-dimensional space, and they have applications in fields such as robotics, computer vision, and quantum mechanics.
Yes, there are many practical applications for these number systems. In addition to their use in science and engineering, they are also used in computer graphics, digital signal processing, and cryptography. They also have applications in game development, creating realistic animations and simulations.