Definition
A number made up of two parts: a real part and an imaginary part, written in the form a + bi, where a and b are real numbers and i represents the square root of -1. Complex numbers are used in electrical and electronic calculations involving alternating current, where quantities have both a magnitude and a phase angle.
Plain English
A number that combines a normal number with a second part used to represent something that ordinary numbers can't, such as the timing relationship between voltage and current in an AC circuit. It lets engineers describe two things at once with a single number.
Context Anchor
Seen in aircraft electrical theory, electronics troubleshooting, and alternating-current circuit discussions.
Derivation
From Latin complexus, meaning 'woven together' or 'combined.' The name reflects that the number is built from two parts joined into one expression.
Why Pilots Care
Pilots don't calculate with complex numbers in the cockpit, but the concept underlies how AC electrical systems and avionics are analyzed and described in maintenance and theory texts.
Analogy
A single number is like saying “go 5 miles.” A complex number is more like saying “go 3 miles east and 4 miles north” — it gives two pieces of information that together describe one value.
Intuition Check
Complex does not mean “complicated” here. It means a number built from two linked parts: a real part and an imaginary part.
Example Sentence 1
The textbook used complex numbers to describe the relationship between voltage and current in the aircraft's AC power system.
Example Sentence 2
Engineers apply complex numbers when calculating phase angles in aircraft radio transmitters.