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
Let $\left({x_1, y_1}\right)$ and $\left({x_2, y_2}\right)$ be complex numbers.

Then $\left({x_1, y_1}\right) + \left({x_2, y_2}\right)$ is defined as:


 * $\left({x_1, y_1}\right) + \left({x_2, y_2}\right):= \left({x_1 + x_2, y_1 + y_2}\right)$

Also see

 * Complex Addition is Commutative
 * Complex Addition is Associative
 * Identity Element of Addition on Numbers
 * Inverse Elements for Addition on Numbers