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Tī sò͘-ha̍k tiong, chi̍t ê ho̍k-cha̍p-sò͘
ê ho̍k-kiōng-tam (Hàn-jī: 複共擔, Eng-gí: complex conjugate)
[1] mā sī chi̍t ê ho̍k-cha̍p-sò͘,
ê si̍t-pó͘ kah
sio-kâng,
hi-pō͘ kah
pêⁿ-tōa tān-sī hû-hō tùi-hoán ê sò͘. Khiā-sǹg-kóng, nā-chún
kap
sī si̍t-sò͘,
ê ho̍k-kiōng-tam tiō sī
. Pí-lūn-kóng,
![{\textstyle {\overline {-4+3i}}=-4-3i}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9EytsQoqzDztlAytJDaNrAnDC1zgi2ngiOzqo5ajJDntK0nAwNnDCP)
(si̍t-sò͘ ê ho̍k-kiōng-tam sī i ka-kī)
(sûn hi-sò͘ ê ho̍k-kiōng-tam sī i ê tùi-hoán sò͘)
Lán nā iōng-tio̍h ke̍k-chò-piau piáu-sī, ē-sái án-ne tēng-gī ho̍k-kiōng-tam:
![{\displaystyle {\overline {re^{i\theta }}}=re^{-i\theta }}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8QoqaNaNa2yteNaNvFntwNzNK4zNs1yjaOa2e0z2a0nDJByje5otmN)
kî-tiong in ê hok-kak hû-hō tùi-hoán. Che ē-sái iōng Euler kong-sek lâi chèng-bêng.
Eng-gí conjugate goân-chū Latin-gí ê coniugāre (“liân chò-hóe, gû-taⁿ”), iû con- (“chò-hóe”) + iugāre (“ chiap, pa̍k, liân”) kò͘-sêng.
Tiong-kok-ōe kā e̍k-chò 共軛. Ji̍t-pún-ōe e̍k-chò 共役. Tâi-oân-ōe e̍k-chò 共擔.
Ho̍k-kiōng-tam ê kì-hō ū nn̄g chióng: vinculum
kap chheⁿ-tiám
.
Tē 1 chióng sò͘-ha̍k-ka khah ài iōng.
Tē 2 chióng bu̍t-lí-ha̍k, tiān-ki kang-têng, tiān-náu kho-ha̍k téng-téng léng-he̍k khah ài iōng.
Chi̍t ê ho̍k hâng-lia̍t ê ho̍k-kiōng-tam tiō sī ta̍k-ê iàu-sò͘ lóng ka i piàn-chò ho̍k-kiōng-tam. Pí-lūn-kóng,
![{\displaystyle \mathbf {A} ={\begin{pmatrix}2+3i&{\sqrt {3}}i\\1-0.5i&-6\end{pmatrix}},\quad {\overline {\mathbf {A} }}={\begin{pmatrix}2-3i&-{\sqrt {3}}i\\1+0.5i&-6\end{pmatrix}}.}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO9DntiPagi3zqs2nqo0yjK2ntCOnjGOntdDzjm2ygrCaqa5yjiQaNFB)
Tùi jīm-hô nn̄g ê ho̍k-cha̍p-sò͘
kap
, lán ū
.
.
.
.
, chún-kóng
.
.
.
, chún-kóng
.
, tùi só͘-ū ê ![{\displaystyle n\in \mathbb {Z} }](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8NoNhDnDnFztiNnDeQzDe1aNhCytrCoAePytG5zjw5aNnAaNiOytGO)
![{\displaystyle \exp \left({\overline {z}}\right)={\overline {\exp(z)}}}](https://amansaja.com/index.php?q=Mfv0Kfa6bO93MqTXLqrCMqiSL3dZb2hQMu9Onpz0p3oPb21BngBFb21FJgGRKArSngrOb3z2nO8QyjlEzqrBngnBoNs4ageNaNe5oDm3zjJAnAsOoAi1yqi4ztK5aAa2)
, chún-kóng
.
- ↑ ēng Eng-gí tha̍k-chò “z bar”.