# Definition of imaginary number in US English:

## imaginary number

### noun

Mathematics
• A number that is expressed in terms of the square root of a negative number (usually the square root of −1, represented by i or j)

‘when imaginary numbers are squared, they yield a negative result’
• ‘Another very significant application of the imaginary number to the physical world comes from quantum theory.’
• ‘Historically, imaginary numbers first came to light when trying to solve cubic equations, rather than quadratics.’
• ‘Using a combination of real and imaginary numbers, known as complex numbers, turns out to be sufficient to solve virtually all mathematical problems!’
• ‘In the first Knuth describes an imaginary number system using the imaginary number 2i as its base, giving methods for the addition, subtraction and multiplication of the numbers.’
• ‘Imaginary numbers (such as the square root of minus one) form a direct component of the wave amplitude, and thus the probability function, of a wave/particle.’