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Imaginary number

The name "imaginary number" was first used in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless, but today they have a variety of essential, concrete applications in science and engineering.

An imaginary number is a number whose square is less than or equal to zero.

For example, is an imaginary number and its square is −25.

An imaginary number can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1

An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where a and b are called, respectively, the real part and the imaginary part of the complex number.

Imaginary numbers can therefore be thought of as complex numbers whose real part is zero.