OB1, following are a few clues. First this is only a little trickier than algebra. If you coped with algebra and spent some time concentrating on this stuff, it would not seem so tuff.

Mathematicians got upset well over 100 years ago because simple equations like "X^2 + 1 = 0" had no solution. So they invented something called complex numbers.

The idea is that "i" is defined as the square root of -1. Using this definition, a complex number is (a + ib) or (x + iy). where a, b, x, & y are ordinary numbers, and i is the square root of minus one. There are definitions for addition, subtraction, multiplication, and division of complex numbers.

The above worked pretty good, and was useful for many practical purposes.

Quaternions are an extension of the above idea. A quaternion is (a + ib + jc + kd), where a, b, c, & d are ordinary numbers; i^2 = j^2 = k^2 = -1; i*j = k, j*k = i, & k*i = j. The tricky gimmick here is that j*i = -k, k*j = -i, i*k = -j. Changing the order of multiplication of i, j, k changes the sign of the product.

It seems weird at first, but it works. There are definitions for add, subtract, multiply, & divide of quaternions.