Definition:Complex Number/Wholly Imaginary

Definition

A complex number $z = a + i b$ is wholly imaginary if and only if $a = 0$.

Also known as

Variants on wholly imaginary are:

completely imaginary

entirely imaginary

purely imaginary

a pure imaginary number

and so on.

Also see

• Definition:Wholly Real

• Results about wholly imaginary can be found here.

Sources

• 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 1.2$. The Algebraic Theory
• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $1$: Complex Numbers: The Complex Number System
• 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
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): imaginary number