z=(a+5)i^6+(a-3)i^7 eching

$$z = ( a + 5 ) i ^ { 6 } + ( a - 3 ) i ^ { 7 }$$

a uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

6 daraja ko‘rsatkichini i ga hisoblang va -1 ni qiymatni oling.

$$z=\left(a+5\right)\left(-1\right)+\left(a-3\right)i^{7}$$

a+5 ga -1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$z=-a-5+\left(a-3\right)i^{7}$$

7 daraja ko‘rsatkichini i ga hisoblang va -i ni qiymatni oling.

$$z=-a-5+\left(a-3\right)\left(-i\right)$$

a-3 ga -i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$z=-a-5-ia+3i$$

\left(-1-i\right)a ni olish uchun -a va -ia ni birlashtirish.

$$z=\left(-1-i\right)a-5+3i$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\left(-1-i\right)a-5+3i=z$$

5 ni ikki tarafga qo’shing.

$$\left(-1-i\right)a+3i=z+5$$

Ikkala tarafdan 3i ni ayirish.

$$\left(-1-i\right)a=z+5-3i$$

Tenglama standart shaklda.

$$\left(-1-i\right)a=z+\left(5-3i\right)$$

Ikki tarafini -1-i ga bo‘ling.

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

-1-i ga bo'lish -1-i ga ko'paytirishni bekor qiladi.

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

z+\left(5-3i\right) ni -1-i ga bo'lish.

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

z uchun yechish

$$z=\left(-1-i\right)a+\left(-5+3i\right)$$