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

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

Baholash

$$\frac{824}{169}+\frac{389}{169}i\approx 4,875739645+2,301775148i$$

Yechim qadamlari

3 daraja ko‘rsatkichini 1+4i ga hisoblang va -47-52i ni qiymatni oling.

$$\frac{i\left(-47-52i\right)}{\left(3-2i\right)^{2}}$$

52-47i hosil qilish uchun i va -47-52i ni ko'paytirish.

$$\frac{52-47i}{\left(3-2i\right)^{2}}$$

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

$$\frac{52-47i}{5-12i}$$

Ham hisoblagich, ham maxrajni maxraj kompleksiga murakkablash orqali ko'paytirish, 5+12i.

$$\frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)}$$

\frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)} ichidagi ko‘paytirishlarni bajaring.

$$\frac{824+389i}{169}$$

\frac{824}{169}+\frac{389}{169}i ni olish uchun 824+389i ni 169 ga bo‘ling.

$$\frac{824}{169}+\frac{389}{169}i$$

Ashyoviy qism

$$\frac{824}{169} = 4\frac{148}{169} = 4,875739644970414$$

Yechim qadamlari

3 daraja ko‘rsatkichini 1+4i ga hisoblang va -47-52i ni qiymatni oling.

$$Re(\frac{i\left(-47-52i\right)}{\left(3-2i\right)^{2}})$$

52-47i hosil qilish uchun i va -47-52i ni ko'paytirish.

$$Re(\frac{52-47i}{\left(3-2i\right)^{2}})$$

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

$$Re(\frac{52-47i}{5-12i})$$

\frac{52-47i}{5-12i}ning surat va maxrajini murakkab tutash maxraj 5+12i bilan ko‘paytiring.

$$Re(\frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)})$$

\frac{\left(52-47i\right)\left(5+12i\right)}{\left(5-12i\right)\left(5+12i\right)} ichidagi ko‘paytirishlarni bajaring.

$$Re(\frac{824+389i}{169})$$

\frac{824}{169}+\frac{389}{169}i ni olish uchun 824+389i ni 169 ga bo‘ling.

$$Re(\frac{824}{169}+\frac{389}{169}i)$$

\frac{824}{169}+\frac{389}{169}i ning real qismi – \frac{824}{169}.

$$\frac{824}{169}$$