z=1+3i/2-i(i) eching

$$z = \frac { 1 + 3 i } { 2 - i } ( i )$$

z uchun yechish

$$z=-\frac{7}{5}-\frac{1}{5}i=-1,4-0,2i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{1+3i}{2-i}ning surat va maxrajini murakkab tutash maxraj 2+i bilan ko‘paytiring.

$$z=\frac{\left(1+3i\right)\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}i$$

Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$z=\frac{\left(1+3i\right)\left(2+i\right)}{2^{2}-i^{2}}i$$

Ta’rifi bo‘yicha, i^{2} – bu -1. Maxrajini hisoblang.

$$z=\frac{\left(1+3i\right)\left(2+i\right)}{5}i$$

Binomlarni ko‘paytirgandek 1+3i va 2+i murakkab sonlarni ko‘paytiring.

$$z=\frac{1\times 2+i+3i\times 2+3i^{2}}{5}i$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$z=\frac{1\times 2+i+3i\times 2+3\left(-1\right)}{5}i$$

1\times 2+i+3i\times 2+3\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$z=\frac{2+i+6i-3}{5}i$$

2+i+6i-3 ichida real va mavhum qismlarni birlashtiring.

$$z=\frac{2-3+\left(1+6\right)i}{5}i$$

2-3+\left(1+6\right)i ichida qo‘shishlarni bajaring.

$$z=\frac{-1+7i}{5}i$$

-\frac{1}{5}+\frac{7}{5}i ni olish uchun -1+7i ni 5 ga bo‘ling.

$$z=\left(-\frac{1}{5}+\frac{7}{5}i\right)i$$

-\frac{1}{5}+\frac{7}{5}i ni i marotabaga ko'paytirish.

$$z=-\frac{1}{5}i+\frac{7}{5}i^{2}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$z=-\frac{1}{5}i+\frac{7}{5}\left(-1\right)$$

-\frac{1}{5}i+\frac{7}{5}\left(-1\right) ichidagi ko‘paytirishlarni bajaring. Shartlarni qayta saralash.

$$z=-\frac{7}{5}-\frac{1}{5}i$$

z'ni tayinlash

$$z≔-\frac{7}{5}-\frac{1}{5}i$$