## i

The Imaginary Number is defined as . However, for some reason engineers and physicists prefer the symbol j to . Numbers of the form where and are Real Numbers are called Complex Numbers, and when is used to denote a Complex Number, it is sometimes (in older texts) called an Affix.''

The Square Root of is

 (1)

since
 (2)

This can be immediately derived from the Euler Formula with ,
 (3)

 (4)

The Principal Value of is

 (5)

See also Complex Number, Imaginary Identity, Imaginary Number, Real Number, Surreal Number

References

Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 89, 1996.