Editing Complex number (section)

===Multiplication{{anchor|Multiplication|Square}}===
The product of two complex numbers is computed as follows:
:<math>(a+bi) \cdot (c+di) = ac - bd + (ad+bc)i.</math>
For example, <math>(3+2i)(4-i) = 3 \cdot 4 - (2 \cdot (-1)) + (3 \cdot (-1) + 2 \cdot 4)i = 14 +5i.</math> 
In particular, this includes as a special case the fundamental formula
:<math>i^2 = i \cdot i = -1.</math>
This formula distinguishes the complex number ''i'' from any real number, since the square of any (negative or positive) real number is always a non-negative real number.

With this definition of multiplication and addition, familiar rules for the arithmetic of rational or real numbers continue to hold for complex numbers. More precisely, the [[distributive property]], the [[commutative property|commutative properties]] (of addition and multiplication) hold. Therefore, the complex numbers form an algebraic structure known as a [[field (mathematics)|''field'']], the same way as the rational or real numbers do.{{sfn|Apostol|1981|pp=15–16}}