Quaternions

In my last Geometer’s Corner, I focused on how rotations can be expressed using complex numbers and 3 × 3 matrices. We saw that you can use the complex number sin(t) + cos(t)i as an operator that will rotate any complex number a + bi through an angle of t degrees. In what follows it will be useful to think of a + bi as an ordered pair (a, bi) where a is real number and bi is a complex number with i² = –1.