Razlika između inačica stranice »Imaginarna jedinica«
(nova stranica: {{lowercase}} {{HNM2 pojam |naziv=imaginarna jedinica |naziv2=imaginarna-jedinica |Struna_ID=33176 |obrađivač=Magdakena Igaly |faza_obrade=zaključaj naziv |definicija=imaginarna...) |
|||
Redak 9: | Redak 9: | ||
|školska_definicija= | |školska_definicija= | ||
|šd_obrađivač= | |šd_obrađivač= | ||
− | |napomena=<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> | + | |napomena=<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^{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>, ... | 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 | ||
|broj=jednina | |broj=jednina | ||
− | |simbol= | + | |simbol=<math>i</math> |
|kontekst= | |kontekst= | ||
|dopušteni= | |dopušteni= | ||
Redak 26: | Redak 26: | ||
|suprotnica= | |suprotnica= | ||
|zastarjeli= | |zastarjeli= | ||
− | |povezani= | + | |povezani=[[čisto imaginarni broj]], [[kompleksni broj]] |
}} | }} | ||
Redak 32: | Redak 32: | ||
|Struna_ID=33176 | |Struna_ID=33176 | ||
|naziv=imaginary unit | |naziv=imaginary unit | ||
− | |klasifikacija= | + | |klasifikacija=Calculus and Analysis > Complex Analysis > Complex Numbers > |
− | |definicija= | + | |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>. |
− | |cite= | + | |cite=Weisstein, Eric W. "Imaginary Unit." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ImaginaryUnit.html |
− | |napomena= | + | |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>. |
− | |see_also= | + | |see_also= Complex Number, i, Imaginary Number, Unit |
|primjeri= | |primjeri= | ||
}} | }} |
Inačica od 21:06, 3. listopada 2016.
Definicija: imaginarna jedinica \(i\) se definira kao broj koji kvadriran daje \(–1\)
Napomena: \(i^{0}=1\), \(i^{1}=i=\sqrt{-1}\), \(i^{2}=-1\), \(i^{3}=i^{2}\cdot i=\left ( -1 \right )\cdot i=-i\), \( i^{4}=i^{2}\cdot i^{2}=\left ( -1 \right )\cdot\left ( -1 \right )=1\), \(i^{5}=i^{4}\cdot i=1\cdot i=i\), \( i^{6}=i^{4}\cdot i^{2}\cdot=1\cdot \left ( -1 \right )=-1\), ...
Povezani pojmovi: čisto imaginarni broj, kompleksni broj
Simbol: \(i\)
Engleske istovrijednice: imaginary unit
Struna ID: 33176
Obrađivač: Magdakena 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