Definition:Subtraction/Complex Numbers

Definition

Let $\struct {\C, +, \times}$ be the field of complex numbers.

The operation of subtraction is defined on $\C$ as:

$\forall a, b \in \C: a - b := a + \paren {-b}$

where $-b$ is the negative of $b$ in $\C$.

Examples

Example: $\paren {8 - 6 i} - \paren {2 i - 7}$

$\paren {8 - 6 i} - \paren {2 i - 7} = 15 - 8 i$

Example: $\paren {6 - 2 i} - \paren {2 - 5 i}$

$\paren {6 - 2 i} - \paren {2 - 5 i} = 4 + 3 i$

Also see

• Subtraction of Complex Numbers

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 $(3)$
• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complex number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complex number