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Imaginary part - Definition and Overview |
| Related Words: Abstract, Airy, Algorithmic, Autistic, Cardinal, Deceptive, Decimal, Delusional, Differential, Digital, Dreamlike, Ethereal |
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In mathematics, the imaginary part of a complex number z is the second element of the ordered pair of real numbers representing z, i.e. if <math>z=x+\mathrm{i}y<math> then the imaginary part of <math>z<math> is <math>y<math>.
In terms of the complex conjugate <math>\bar{z}<math>, the imaginary part of z is equal to <math>\frac{z-\bar{z}}{2\mathrm{i}}.<math>
The imaginary part of <math>z<math> is denoted <math>\mbox{Im}z<math> or <math>\Im z<math>. It is not holomorphic.
If a complex number is written as <math>re^{\mathrm{i}\theta}<math>, then the imaginary part is <math>r\sin\theta<math>. (See Euler's formula.)
See also
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