The real number system is such that not every equation can be solved in terms of real numbers. Thus the simple algebraic equation


has no solution in terms of real numbers. To overcome this limitation, the

real number system is extended to become the complex number system, and

this is accomplished by introducing the unit imaginary element i defined as

/ i(1): In terms of this so-called imaginary element, the equation x2/1/0,

which may be written as

x21, or as x9(1),

is seen to have the solutions /x9i: Similarly, the equation x2/16/0 may be rewritten as

x216, or as x9(16):

If we write /16/16/(/1), this last result becomes


and so the equation is seen to have the two imaginary solutions x/4i and x// 4i.