Are all complex numbers quaternions?

Absolutely, unequivocally, not. Complex numbers are one of the cornerstones of modern mathematics, whereas the Quaternions are a way to generate division algebras.

Is there anything beyond complex numbers?

Complex numbers include both real numbers, whose imaginary part is zero (such as pi and zero), and imaginary numbers, whose real part is zero (such as the square root of negative one). All numbers are of these types, so there is nothing beyond complex numbers.

What concepts do complex numbers help with?

Uses of complex numbers Complex numbers can be used to solve quadratics for zeroes. The quadratic formula solves ax2 + bx + c = 0 for the values of x. If the formula provides a negative in the square root, complex numbers can be used to simplify the zero. Complex numbers are used in electronics and electromagnetism.

Why are quaternions useful?

Quaternions are vital for the control systems that guide aircraft and rockets. Each quaternion has an axis giving its direction and a magnitude giving the size of the rotation. Instead of representing a change of orientation by three separate rotations, quaternions use just one rotation.

Are the quaternions a ring?

The ring of real quaternions is a division ring. (Recall that a division ring is a unital ring in which every element has a multiplicative inverse. A division ring that is commutative is simply a field.)

How do electrical engineers use complex numbers?

The conjugate of a complex number is an important element used in Electrical Engineering to determine the apparent power of an AC circuit using rectangular form.

Why are quaternions so hard to understand?

Quaternions extend the 2D rotation properties of complex numbers to 3D, and it’s necessary to do that extension because complex numbers don’t have the necessary properties of 3 dimensions. There’s another way to extend complex numbers to get quaternions that doesn’t involve rotations.

What does a quaternion represent?

A quaternion represents two things. It has an x, y, and z component, which represents the axis about which a rotation will occur. It also has a w component, which represents the amount of rotation which will occur about this axis. In short, a vector, and a float.