Imaginary number

The imaginary numbers are a part of the complex numbers. Every complex number can be written as the sum a+bi of a real number a and an imaginary number bi (with real numbers a and b, and the imaginary unit i). In the complex plane the imaginary numbers lie on the imaginary axes. perpendicular to the real axes,

However, sometimes the term "imaginary" is used more generally for all non-real complex numbers, i.e., all numbers with non-vanishing imaginary part (b not 0), are called "imaginary". In this case, the more specific complex numbers bi (with vanishing real part a=0) are called pure(ly) imaginary.

Remark:
The names "imaginary" and "complex" number are of historical origin, just as the other names for numbers — "rational", "irrational", and "real" — are.
Thus they must not be interpreted literally, and no mathematical or philosophical conclusions may be drawn from them.

For more information, see Complex number.