Math 2.0

Functions of a complex variable Definition

Complex conjugate

Builds on Complex numbersReal and imaginary parts

Definition

Let z=a+biz = a + b i be a complex number, with aa and bb real. The complex conjugate of zz is the complex number zˉ=a−bi\bar{z} = a - b i.

Remarks

Another common notation is z∗z^*. Conjugation respects the operations: z+w‾=zˉ+wˉ\overline{z + w} = \bar{z} + \bar{w} and zw‾=zˉ wˉ\overline{z w} = \bar{z} \, \bar{w}. Also zˉˉ=z\bar{\bar{z}} = z. A complex number zz is real exactly when zˉ=z\bar{z} = z. The product zzˉz \bar{z} is the real number ∣z∣2|z|^2, see a complex number times its conjugate.

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Where this leads

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Further reading

  1. Web https://en.wikipedia.org/wiki/Complex_conjugate, lead section
  2. Web https://en.wikipedia.org/wiki/Complex_conjugate, Notation
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