Imaginary number: Difference between revisions
imported>Peter Schmitt (starting rewriting) |
imported>Peter Schmitt (expanding remark on literal meaning) |
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(with vanishing real part ''a''=0) are called '''pure(ly) imaginary'''. | (with vanishing real part ''a''=0) are called '''pure(ly) imaginary'''. | ||
'''Remark:'''<br> | |||
The names "imaginary" and "complex" number are of historical origin, | |||
just as the other names for numbers | |||
— "[[rational number|rational]]", "[[irrational number|irrational]]", and "[[real number|real]]" — are. | |||
<br> | |||
Thus they must not be interpreted literally, | |||
and no mathematical or philosophical conclusions may be drawn from them. | |||
For more information, see '''[[Complex number]]'''. | For more information, see '''[[Complex number]]'''. | ||
Revision as of 21:25, 31 December 2009
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.