With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

III.76 Quaternions, Octonions, and Normed Division Algebras

Mathematics took a leap forward in sophistication with the introduction of the COMPLEX NUMBERS [I.3 §1.5]. To define these, one suspends one’s disbelief, introduces a new number i, and declares that i2 = -1. A typical complex number is of the form a + ib, and the arithmetic of complex numbers is easy to deduce from the normal rules of arithmetic for real numbers. For example, to calculate the product of 1 + 2i and 2 + i one simply expands some brackets:

(1 + 2i)(2 + i) 2 + 5i + 2i2 = 5i,

the last equality following from the fact that i2 = -1. One of the great advantages of the complex numbers is that, if complex roots are allowed, every polynomial can be factorized into linear factors: ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required