Definition:Complex Number/Complex Plane/Real Axis

Definition

Let the set $\C$ of complex number be expressed as an ordered pairs on the complex plane.

Complex numbers of the form $\tuple {x, 0}$, being wholly real, appear as points on the $x$-axis.

Hence the $x$-axis of the complex plane is known as the real axis.

Also see

• Definition:Imaginary Axis

Sources

• 1957: Tom M. Apostol: Mathematical Analysis ... (previous) ... (next): Chapter $1$: The Real and Complex Number Systems: $\text{1-4}$: Geometrical representation of real numbers
• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Graphical Representation of Complex Numbers
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): real axis
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): real axis