5(i+3)/(1+2i)(1-2i)*(2i)^4/(1+i)^3 eching

$$\frac { 5 ( i + 3 ) } { ( 1 + 2 i ) ( 1 - 2 i ) } \cdot \frac { ( 2 i ) ^ { 4 } } { ( 1 + i ) ^ { 3 } }$$

Baholash

$$-8-16i$$

Yechim qadamlari

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

$$\frac{5\left(i+3\right)}{5}\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}}$$

5 va 5 ni qisqartiring.

$$\left(i+3\right)\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}}$$

4 daraja ko‘rsatkichini 2i ga hisoblang va 16 ni qiymatni oling.

$$\left(i+3\right)\times \frac{16}{\left(1+i\right)^{3}}$$

3 daraja ko‘rsatkichini 1+i ga hisoblang va -2+2i ni qiymatni oling.

$$\left(i+3\right)\times \frac{16}{-2+2i}$$

\frac{16}{-2+2i}ning surat va maxrajini murakkab tutash maxraj -2-2i bilan ko‘paytiring.

$$\left(i+3\right)\times \frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)}$$

\frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)} ichidagi ko‘paytirishlarni bajaring.

$$\left(i+3\right)\times \frac{-32-32i}{8}$$

-4-4i ni olish uchun -32-32i ni 8 ga bo‘ling.

$$\left(i+3\right)\left(-4-4i\right)$$

i+3 ga -4-4i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$4-4i+\left(-12-12i\right)$$

-8-16i olish uchun 4-4i va -12-12i'ni qo'shing.

$$-8-16i$$

Ashyoviy qism

$$-8$$

Yechim qadamlari

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

$$Re(\frac{5\left(i+3\right)}{5}\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}})$$

5 va 5 ni qisqartiring.

$$Re(\left(i+3\right)\times \frac{\left(2i\right)^{4}}{\left(1+i\right)^{3}})$$

4 daraja ko‘rsatkichini 2i ga hisoblang va 16 ni qiymatni oling.

$$Re(\left(i+3\right)\times \frac{16}{\left(1+i\right)^{3}})$$

3 daraja ko‘rsatkichini 1+i ga hisoblang va -2+2i ni qiymatni oling.

$$Re(\left(i+3\right)\times \frac{16}{-2+2i})$$

\frac{16}{-2+2i}ning surat va maxrajini murakkab tutash maxraj -2-2i bilan ko‘paytiring.

$$Re(\left(i+3\right)\times \frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)})$$

\frac{16\left(-2-2i\right)}{\left(-2+2i\right)\left(-2-2i\right)} ichidagi ko‘paytirishlarni bajaring.

$$Re(\left(i+3\right)\times \frac{-32-32i}{8})$$

-4-4i ni olish uchun -32-32i ni 8 ga bo‘ling.

$$Re(\left(i+3\right)\left(-4-4i\right))$$

i+3 ga -4-4i ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$Re(4-4i+\left(-12-12i\right))$$

-8-16i olish uchun 4-4i va -12-12i'ni qo'shing.

$$Re(-8-16i)$$

-8-16i ning real qismi – -8.

$$-8$$