(2+i)*z-(3-2i)/2z=4+3i-(2-5i)z eching

$$( 2 + i ) \cdot z - \frac { ( 3 - 2 i ) } { 2 } z = 4 + 3 i - ( 2 - 5 i ) z$$

z uchun yechish

$$z=\frac{4}{61}+\frac{78}{61}i\approx 0,06557377+1,278688525i$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\frac{3}{2}-i ni olish uchun 3-2i ni 2 ga bo‘ling.

$$\left(2+i\right)z-\left(\frac{3}{2}-i\right)z=4+3i-\left(2-5i\right)z$$

\left(\frac{1}{2}+2i\right)z ni olish uchun \left(2+i\right)z va \left(-\frac{3}{2}+i\right)z ni birlashtirish.

$$\left(\frac{1}{2}+2i\right)z=4+3i-\left(2-5i\right)z$$

\left(2-5i\right)z ni ikki tarafga qo’shing.

$$\left(\frac{1}{2}+2i\right)z+\left(2-5i\right)z=4+3i$$

\left(\frac{5}{2}-3i\right)z ni olish uchun \left(\frac{1}{2}+2i\right)z va \left(2-5i\right)z ni birlashtirish.

$$\left(\frac{5}{2}-3i\right)z=4+3i$$

Ikki tarafini \frac{5}{2}-3i ga bo‘ling.

$$z=\frac{4+3i}{\frac{5}{2}-3i}$$

\frac{4+3i}{\frac{5}{2}-3i}ning surat va maxrajini murakkab tutash maxraj \frac{5}{2}+3i bilan ko‘paytiring.

$$z=\frac{\left(4+3i\right)\left(\frac{5}{2}+3i\right)}{\left(\frac{5}{2}-3i\right)\left(\frac{5}{2}+3i\right)}$$

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

$$z=\frac{\left(4+3i\right)\left(\frac{5}{2}+3i\right)}{\left(\frac{5}{2}\right)^{2}-3^{2}i^{2}}$$

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

$$z=\frac{\left(4+3i\right)\left(\frac{5}{2}+3i\right)}{\frac{61}{4}}$$

Binomlarni ko‘paytirgandek 4+3i va \frac{5}{2}+3i murakkab sonlarni ko‘paytiring.

$$z=\frac{4\times \frac{5}{2}+4\times \left(3i\right)+3i\times \frac{5}{2}+3\times 3i^{2}}{\frac{61}{4}}$$

Ta’rifi bo‘yicha, i^{2} – bu -1.

$$z=\frac{4\times \frac{5}{2}+4\times \left(3i\right)+3i\times \frac{5}{2}+3\times 3\left(-1\right)}{\frac{61}{4}}$$

4\times \frac{5}{2}+4\times \left(3i\right)+3i\times \frac{5}{2}+3\times 3\left(-1\right) ichidagi ko‘paytirishlarni bajaring.

$$z=\frac{10+12i+\frac{15}{2}i-9}{\frac{61}{4}}$$

10+12i+\frac{15}{2}i-9 ichida real va mavhum qismlarni birlashtiring.

$$z=\frac{10-9+\left(12+\frac{15}{2}\right)i}{\frac{61}{4}}$$

10-9+\left(12+\frac{15}{2}\right)i ichida qo‘shishlarni bajaring.

$$z=\frac{1+\frac{39}{2}i}{\frac{61}{4}}$$

\frac{4}{61}+\frac{78}{61}i ni olish uchun 1+\frac{39}{2}i ni \frac{61}{4} ga bo‘ling.

$$z=\frac{4}{61}+\frac{78}{61}i$$