Razlika između inačica stranice »Imaginarna jedinica«
| (Nisu prikazane 3 međuinačice 2 suradnika) | |||
| Redak 4: | Redak 4: | ||
|naziv2=imaginarna-jedinica | |naziv2=imaginarna-jedinica | ||
|Struna_ID=33176 | |Struna_ID=33176 | ||
| − | |obrađivač= | + | |obrađivač=Magdalena Igaly |
|faza_obrade=zaključaj naziv | |faza_obrade=zaključaj naziv | ||
| − | |definicija=imaginarna jedinica <math>i</math> se definira kao broj koji [[kvadrat broja|kvadriran]] daje <math>–1</math> | + | |definicija='''imaginarna jedinica''' <math>i</math> se definira kao broj koji [[kvadrat broja|kvadriran]] daje <math>–1</math> |
|školska_definicija= | |školska_definicija= | ||
|šd_obrađivač= | |šd_obrađivač= | ||
| − | |napomena=Nekoliko početnih potencija od <math>i</math> : <math>i^{0}=1</math> : <math>i^{1}=i=\sqrt{-1}</math> | + | |napomena=Nekoliko početnih [[potencija]] od <math>i</math> : <math>i^{0}=1</math> : <math>i^{1}=i=\sqrt{-1}</math> : <math>i^{2}=-1</math> : <math>i^{3}=i^{2}\cdot i=\left ( -1 \right )\cdot i=-i</math> : <math>i^{4}=i^{2}\cdot i^{2}=\left ( -1 \right )\cdot\left ( -1 \right )=1</math> : <math>i^{5}=i^{4}\cdot i=1\cdot i=i</math> : <math>i^{6}=i^{4}\cdot i^{2}\cdot=1\cdot \left ( -1 \right )=-1</math> |
|vrsta_riječi=imenica | |vrsta_riječi=imenica | ||
|rod=ženski | |rod=ženski | ||
| Redak 31: | Redak 31: | ||
|naziv=imaginary unit | |naziv=imaginary unit | ||
|klasifikacija=Calculus and Analysis > Complex Analysis > Complex Numbers > | |klasifikacija=Calculus and Analysis > Complex Analysis > Complex Numbers > | ||
| − | |definicija=The imaginary number <math>i=\sqrt{-1}</math>, i.e., the square root of <math>-1</math>. The imaginary unit is denoted and commonly referred to as <math>i</math>. | + | |definicija=The imaginary number <math>i=\sqrt{-1}</math>, i.e., the [[drugi korijen|square root]] of <math>-1</math>. The imaginary unit is denoted and commonly referred to as <math>i</math>. |
|cite=Weisstein, Eric W. "Imaginary Unit." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ImaginaryUnit.html | |cite=Weisstein, Eric W. "Imaginary Unit." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ImaginaryUnit.html | ||
| − | |napomena=Although there are two possible square roots of any number, the square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point <math>+i</math> and <math>-i</math> can then be distinguished. Since either choice is possible, there is no ambiguity in defining <math>i</math> as "the" square root of <math>-1</math>. | + | |napomena=Although there are two possible square roots of any number, the square roots of a [[negativni broj|negative number]] cannot be distinguished until one of the two is defined as the imaginary unit, at which point <math>+i</math> and <math>-i</math> can then be distinguished. Since either choice is possible, there is no ambiguity in defining <math>i</math> as "the" square root of <math>-1</math>. |
|see_also= Complex Number, i, Imaginary Number, Unit | |see_also= Complex Number, i, Imaginary Number, Unit | ||
|primjeri= | |primjeri= | ||
}} | }} | ||
Trenutačna izmjena od 16:52, 12. listopada 2016.
Definicija: imaginarna jedinica \(i\) se definira kao broj koji kvadriran daje \(–1\)
Napomena: Nekoliko početnih potencija od \(i\) \[i^{0}=1\] \[i^{1}=i=\sqrt{-1}\] \[i^{2}=-1\] \[i^{3}=i^{2}\cdot i=\left ( -1 \right )\cdot i=-i\] \[i^{4}=i^{2}\cdot i^{2}=\left ( -1 \right )\cdot\left ( -1 \right )=1\] \[i^{5}=i^{4}\cdot i=1\cdot i=i\] \[i^{6}=i^{4}\cdot i^{2}\cdot=1\cdot \left ( -1 \right )=-1\]
Povezani pojmovi: čisto imaginarni broj, kompleksni broj
Simbol: \(i\)
Engleske istovrijednice: imaginary unit
Struna ID: 33176
Obrađivač: Magdalena Igaly
Faza obrade: zaključaj naziv
Vrsta riječi: imenica Rod: ženski Broj: jednina
Cilj projekta "Hrvatsko nazivlje u matematici" je na jednom mjestu prikupiti i obraditi sve hrvatske nazive koji na izravan ili neizravan način imaju veze s matematikom. Ako želite na bilo koji način doprinijeti ostvarenju ciljeva ovog projekta, molim javite se voditelju projekta na adresu goran.igaly@math.hr
WMW naziv: imaginary unit
WMW klasifikacija: Calculus and Analysis > Complex Analysis > Complex Numbers >
WMW definicija: The imaginary number \(i=\sqrt{-1}\), i.e., the square root of \(-1\). The imaginary unit is denoted and commonly referred to as \(i\).
WMW napomena: Although there are two possible square roots of any number, the square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point \(+i\) and \(-i\) can then be distinguished. Since either choice is possible, there is no ambiguity in defining \(i\) as "the" square root of \(-1\).
WMW See also: Complex Number, i, Imaginary Number, Unit
Izvor: Weisstein, Eric W. "Imaginary Unit." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ImaginaryUnit.html
Struna ID: 33176