Definition:Addition/Complex Numbers

Definition
The addition operation in the domain of complex numbers $\C$ is written $+$.

Let $z = a + i b, w = c + i d$ where $a, b, c, d \in \R, i^2 = -1$.

Then $z + w$ is defined as:
 * $\left({a + i b}\right) + \left({c + i d}\right) = \left({a + c}\right) + i \left({b + d}\right)$

Complex Addition
When the formal definition of complex numbers is used, complex addition is defined thus:

Also see

 * Complex Addition is Commutative
 * Complex Addition is Associative


 * Identity Element of Addition on Numbers
 * Inverse Elements for Addition on Numbers


 * Definition:Complex Multiplication