Definition:Addition/Complex Numbers

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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:


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:

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


Examples

Example: $\left({3 + 2 i}\right) + \left({5 + 6 i}\right)$

$\left({3 + 2 i}\right) + \left({5 + 6 i}\right) = 8 + 8 i$


Example: $\left({-1 + 4 i}\right) + \left({2 + \left({-7}\right) i}\right)$

$\left({-1 + 4 i}\right) + \left({2 + \left({-7}\right) i}\right) = 1 + \left({-3}\right) i$


Also see


Sources