Baholash
\frac{3}{5}-\frac{4}{5}i=0,6-0,8i
Ashyoviy qism
\frac{3}{5} = 0,6
Viktorina
Complex Number
5xshash muammolar:
\frac { ( 4 + 3 i ) ( 1 - 2 i ) } { ( 4 - 3 i ) ( 1 + 2 i ) }
Baham ko'rish
Klipbordga nusxa olish
\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)i^{2}}{\left(4-3i\right)\left(1+2i\right)}
Binomlarni ko‘paytirgandek 4+3i va 1-2i murakkab sonlarni ko‘paytiring.
\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right)}{\left(4-3i\right)\left(1+2i\right)}
Ta’rifi bo‘yicha, i^{2} – bu -1.
\frac{4-8i+3i+6}{\left(4-3i\right)\left(1+2i\right)}
4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.
\frac{4+6+\left(-8+3\right)i}{\left(4-3i\right)\left(1+2i\right)}
4-8i+3i+6 ichida real va mavhum qismlarni birlashtiring.
\frac{10-5i}{\left(4-3i\right)\left(1+2i\right)}
4+6+\left(-8+3\right)i ichida qo‘shishlarni bajaring.
\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2i^{2}}
Binomlarni ko‘paytirgandek 4-3i va 1+2i murakkab sonlarni ko‘paytiring.
\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right)}
Ta’rifi bo‘yicha, i^{2} – bu -1.
\frac{10-5i}{4+8i-3i+6}
4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.
\frac{10-5i}{4+6+\left(8-3\right)i}
4+8i-3i+6 ichida real va mavhum qismlarni birlashtiring.
\frac{10-5i}{10+5i}
4+6+\left(8-3\right)i ichida qo‘shishlarni bajaring.
\frac{\left(10-5i\right)\left(10-5i\right)}{\left(10+5i\right)\left(10-5i\right)}
Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 10-5i.
\frac{\left(10-5i\right)\left(10-5i\right)}{10^{2}-5^{2}i^{2}}
Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{\left(10-5i\right)\left(10-5i\right)}{125}
Ta’rifi bo‘yicha, i^{2} – bu -1. Maxrajini hisoblang.
\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)i^{2}}{125}
Binomlarni ko‘paytirgandek 10-5i va 10-5i murakkab sonlarni ko‘paytiring.
\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right)}{125}
Ta’rifi bo‘yicha, i^{2} – bu -1.
\frac{100-50i-50i-25}{125}
10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.
\frac{100-25+\left(-50-50\right)i}{125}
100-50i-50i-25 ichida real va mavhum qismlarni birlashtiring.
\frac{75-100i}{125}
100-25+\left(-50-50\right)i ichida qo‘shishlarni bajaring.
\frac{3}{5}-\frac{4}{5}i
\frac{3}{5}-\frac{4}{5}i ni olish uchun 75-100i ni 125 ga bo‘ling.
Re(\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)i^{2}}{\left(4-3i\right)\left(1+2i\right)})
Binomlarni ko‘paytirgandek 4+3i va 1-2i murakkab sonlarni ko‘paytiring.
Re(\frac{4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right)}{\left(4-3i\right)\left(1+2i\right)})
Ta’rifi bo‘yicha, i^{2} – bu -1.
Re(\frac{4-8i+3i+6}{\left(4-3i\right)\left(1+2i\right)})
4\times 1+4\times \left(-2i\right)+3i\times 1+3\left(-2\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.
Re(\frac{4+6+\left(-8+3\right)i}{\left(4-3i\right)\left(1+2i\right)})
4-8i+3i+6 ichida real va mavhum qismlarni birlashtiring.
Re(\frac{10-5i}{\left(4-3i\right)\left(1+2i\right)})
4+6+\left(-8+3\right)i ichida qo‘shishlarni bajaring.
Re(\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2i^{2}})
Binomlarni ko‘paytirgandek 4-3i va 1+2i murakkab sonlarni ko‘paytiring.
Re(\frac{10-5i}{4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right)})
Ta’rifi bo‘yicha, i^{2} – bu -1.
Re(\frac{10-5i}{4+8i-3i+6})
4\times 1+4\times \left(2i\right)-3i-3\times 2\left(-1\right) ichidagi ko‘paytirishlarni bajaring.
Re(\frac{10-5i}{4+6+\left(8-3\right)i})
4+8i-3i+6 ichida real va mavhum qismlarni birlashtiring.
Re(\frac{10-5i}{10+5i})
4+6+\left(8-3\right)i ichida qo‘shishlarni bajaring.
Re(\frac{\left(10-5i\right)\left(10-5i\right)}{\left(10+5i\right)\left(10-5i\right)})
\frac{10-5i}{10+5i}ning surat va maxrajini murakkab tutash maxraj 10-5i bilan ko‘paytiring.
Re(\frac{\left(10-5i\right)\left(10-5i\right)}{10^{2}-5^{2}i^{2}})
Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
Re(\frac{\left(10-5i\right)\left(10-5i\right)}{125})
Ta’rifi bo‘yicha, i^{2} – bu -1. Maxrajini hisoblang.
Re(\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)i^{2}}{125})
Binomlarni ko‘paytirgandek 10-5i va 10-5i murakkab sonlarni ko‘paytiring.
Re(\frac{10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right)}{125})
Ta’rifi bo‘yicha, i^{2} – bu -1.
Re(\frac{100-50i-50i-25}{125})
10\times 10+10\times \left(-5i\right)-5i\times 10-5\left(-5\right)\left(-1\right) ichidagi ko‘paytirishlarni bajaring.
Re(\frac{100-25+\left(-50-50\right)i}{125})
100-50i-50i-25 ichida real va mavhum qismlarni birlashtiring.
Re(\frac{75-100i}{125})
100-25+\left(-50-50\right)i ichida qo‘shishlarni bajaring.
Re(\frac{3}{5}-\frac{4}{5}i)
\frac{3}{5}-\frac{4}{5}i ni olish uchun 75-100i ni 125 ga bo‘ling.
\frac{3}{5}
\frac{3}{5}-\frac{4}{5}i ning real qismi – \frac{3}{5}.
Misollar
Ikkilik tenglama
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometriya
4 \sin \theta \cos \theta = 2 \sin \theta
Chiziqli tenglama
y = 3x + 4
Arifmetik
699 * 533
Matritsa
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simli tenglama
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differensatsiya
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Oʻngga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Chegaralar
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}