Computing

112 ◾ Computing

French mathematician Jean Le Rond d’Alembert (1717–1783) rst showed

that every polynomial has a complex root, but his proof was not rigorous.

Gauss provided a fully rigorous proof of this result. is is now called the

fundamental theorem of algebra, or the d’Alembert–Gauss theorem. e set of

complex numbers is closed under the arithmetic operations (addition, subtrac-

tion, multiplication, and division). is result was also shown by d’Alembert.

Example 13.1

e addition, subtraction, multiplication, and division of two com-

plex numbers

zaib

1

=+

and

zcdi cd

2

00=+ ≠≠()or

are dened in

the following table:

Operation Denition

Addi ...