z=20t/3-i-(5-3i)*(2+3i)^2+(1+i)^5 eching

$$z = \frac { 20 t } { 3 - i } - ( 5 - 3 i ) \cdot ( 2 + 3 i ) ^ { 2 } + ( 1 + i ) ^ { 5 }$$

t uchun yechish

$$t=\left(\frac{3}{20}-\frac{1}{20}i\right)z+\left(\frac{31}{5}+\frac{111}{10}i\right)$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

\left(6+2i\right)t ni olish uchun 20t ni 3-i ga bo‘ling.

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

2 daraja ko‘rsatkichini 2+3i ga hisoblang va -5+12i ni qiymatni oling.

$$z=\left(6+2i\right)t-\left(5-3i\right)\left(-5+12i\right)+\left(1+i\right)^{5}$$

11+75i hosil qilish uchun 5-3i va -5+12i ni ko'paytirish.

$$z=\left(6+2i\right)t-\left(11+75i\right)+\left(1+i\right)^{5}$$

5 daraja ko‘rsatkichini 1+i ga hisoblang va -4-4i ni qiymatni oling.

$$z=\left(6+2i\right)t-\left(11+75i\right)+\left(-4-4i\right)$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(6+2i\right)t-\left(11+75i\right)+\left(-4-4i\right)=z$$

4+4i ni ikki tarafga qo’shing.

$$\left(6+2i\right)t-\left(11+75i\right)=z+\left(4+4i\right)$$

11+75i ni ikki tarafga qo’shing.

$$\left(6+2i\right)t=z+\left(4+4i\right)+\left(11+75i\right)$$

4+4i+\left(11+75i\right) ichida qo‘shishlarni bajaring.

$$\left(6+2i\right)t=z+15+79i$$

Tenglama standart shaklda.

$$\left(6+2i\right)t=z+\left(15+79i\right)$$

Ikki tarafini 6+2i ga bo‘ling.

$$\frac{\left(6+2i\right)t}{6+2i}=\frac{z+\left(15+79i\right)}{6+2i}$$

6+2i ga bo'lish 6+2i ga ko'paytirishni bekor qiladi.

$$t=\frac{z+\left(15+79i\right)}{6+2i}$$

z+\left(15+79i\right) ni 6+2i ga bo'lish.

$$t=\left(\frac{3}{20}-\frac{1}{20}i\right)z+\left(\frac{31}{5}+\frac{111}{10}i\right)$$

z uchun yechish

$$z=\left(6+2i\right)t+\left(-15-79i\right)$$