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What is Complex Conjugate mean?
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a {\displaystyle a} and b {\displaystyle b} are real, then) the complex conjugate of a + b i {\displaystyle a+bi} is equal to a − b i . {\displaystyle a-bi.} The complex conjugate of z {\displaystyle z} is often denoted as z ¯ . {\displaystyle {\overline {z}}.}
In polar form, the conjugate of r e i φ {\displaystyle re^{i\varphi }} is r e − i φ . {\displaystyle re^{-i\varphi }.} This can be shown using Euler's formula.
The product of a complex number and its conjugate is a real number: a 2 + b 2 {\displaystyle a^{2}+b^{2}} (or r 2 reference
Posted on 06 Dec 2024, this text provides information on Miscellaneous in Maths related to Maths. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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