Definition:Negative/Complex Number
< Definition:Negative(Redirected from Definition:Negative of Complex Number)
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Definition
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:
- $-z = -a - i b$
Examples
The negative of $2 + 3 i$ is $-2 - 3 i$.
The negative of $4 - 5 i$ is $-4 + 5 i$.
Sources
- 1957: E.G. Phillips: Functions of a Complex Variable (8th ed.) ... (previous) ... (next): Chapter $\text I$: Functions of a Complex Variable: $\S 1$. Complex Numbers: $\text {(iii)}$ The fundamental operations $(2)$