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What are imaginary numbers?

MathematicsLesson on requestFree to read

Quick answer

Imaginary numbers are numbers based on the square root of -1, written as i. Since no real number squared gives a negative, mathematicians invented i to solve such equations — and it turns out to be hugely useful in engineering and physics.

Key things to understand

  1. They're built on i, defined as the square root of -1.
  2. No ordinary (real) number squared can give a negative result.
  3. Combined with real numbers they form 'complex numbers'.
  4. They're essential in electronics, signal processing, and physics.

People also ask

What is an imaginary number?
A multiple of i, where i is defined as the square root of -1 — something no real number can be.
Are imaginary numbers actually useful?
Yes — they're vital in electrical engineering, signal processing, quantum physics, and more.
What is a complex number?
A number with a real part and an imaginary part, like 3 + 2i, combining both kinds of number.