frac{1^{80}+i^{12}-3i^26+2i^14}{9+2i-1^35*1^9} eching

$$\frac { 1 ^ { 80 } + i ^ { 12 } - 3 i ^ { 26 } + 2 i ^ { 14 } } { 9 + 2 i - 1 ^ { 35 } \cdot 1 ^ { 9 } }$$

Baholash

$$\frac{6}{17}-\frac{3}{34}i\approx 0,352941176-0,088235294i$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 35 va 9 ni qo‘shib, 44 ni oling.

$$\frac{1^{80}+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

80 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{1+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

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

$$\frac{1+1-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

2 olish uchun 1 va 1'ni qo'shing.

$$\frac{2-3i^{26}+2i^{14}}{9+2i-1^{44}}$$

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

$$\frac{2-3\left(-1\right)+2i^{14}}{9+2i-1^{44}}$$

-3 hosil qilish uchun 3 va -1 ni ko'paytirish.

$$\frac{2-\left(-3\right)+2i^{14}}{9+2i-1^{44}}$$

-3 ning teskarisi 3 ga teng.

$$\frac{2+3+2i^{14}}{9+2i-1^{44}}$$

5 olish uchun 2 va 3'ni qo'shing.

$$\frac{5+2i^{14}}{9+2i-1^{44}}$$

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

$$\frac{5+2\left(-1\right)}{9+2i-1^{44}}$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

$$\frac{5-2}{9+2i-1^{44}}$$

3 olish uchun 5 dan 2 ni ayirish.

$$\frac{3}{9+2i-1^{44}}$$

44 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{3}{9+2i-1}$$

8+2i olish uchun 9+2i dan 1 ni ayirish.

$$\frac{3}{8+2i}$$

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 8-2i.

$$\frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)}$$

\frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)} ichidagi ko‘paytirishlarni bajaring.

$$\frac{24-6i}{68}$$

\frac{6}{17}-\frac{3}{34}i ni olish uchun 24-6i ni 68 ga bo‘ling.

$$\frac{6}{17}-\frac{3}{34}i$$

Ashyoviy qism

$$\frac{6}{17} = 0,35294117647058826$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 35 va 9 ni qo‘shib, 44 ni oling.

$$Re(\frac{1^{80}+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

80 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$Re(\frac{1+i^{12}-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

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

$$Re(\frac{1+1-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

2 olish uchun 1 va 1'ni qo'shing.

$$Re(\frac{2-3i^{26}+2i^{14}}{9+2i-1^{44}})$$

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

$$Re(\frac{2-3\left(-1\right)+2i^{14}}{9+2i-1^{44}})$$

-3 hosil qilish uchun 3 va -1 ni ko'paytirish.

$$Re(\frac{2-\left(-3\right)+2i^{14}}{9+2i-1^{44}})$$

-3 ning teskarisi 3 ga teng.

$$Re(\frac{2+3+2i^{14}}{9+2i-1^{44}})$$

5 olish uchun 2 va 3'ni qo'shing.

$$Re(\frac{5+2i^{14}}{9+2i-1^{44}})$$

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

$$Re(\frac{5+2\left(-1\right)}{9+2i-1^{44}})$$

-2 hosil qilish uchun 2 va -1 ni ko'paytirish.

$$Re(\frac{5-2}{9+2i-1^{44}})$$

3 olish uchun 5 dan 2 ni ayirish.

$$Re(\frac{3}{9+2i-1^{44}})$$

44 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$Re(\frac{3}{9+2i-1})$$

8+2i olish uchun 9+2i dan 1 ni ayirish.

$$Re(\frac{3}{8+2i})$$

\frac{3}{8+2i}ning surat va maxrajini murakkab tutash maxraj 8-2i bilan ko‘paytiring.

$$Re(\frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)})$$

\frac{3\left(8-2i\right)}{\left(8+2i\right)\left(8-2i\right)} ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{24-6i}{68})$$

\frac{6}{17}-\frac{3}{34}i ni olish uchun 24-6i ni 68 ga bo‘ling.

$$Re(\frac{6}{17}-\frac{3}{34}i)$$

\frac{6}{17}-\frac{3}{34}i ning real qismi – \frac{6}{17}.

$$\frac{6}{17}$$