Definition:Negative/Complex Number

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As the Complex Numbers cannot be Ordered Compatibly with Ring Structure, the concept of a negative complex number, relative to a specified zero, is not defined.

However, the negative of a complex number is defined as follows:

Let $z = a + i b$ be a complex number.

Then the negative of $z$ is defined as:

$-z = -a - i b$


The negative of $2 + 3 i$ is $-2 - 3 i$.

The negative of $4 - 5 i$ is $-4 + 5 i$.