240/25+25sqrt{3i+10+sqrt{300}i} eching

$$\frac{ 240 }{ 25+25 \sqrt{ 3 } i+10+ \sqrt{ 300 } i }$$

Baholash

$$\frac{48}{7\left(1+\sqrt{3}i\right)}\approx 1,714285714-2,969229956i$$

Yechim qadamlari

35 olish uchun 25 va 10'ni qo'shing.

$$\frac{240}{35+25i\sqrt{3}+i\sqrt{300}}$$

Faktor: 300=10^{2}\times 3. \sqrt{10^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{10^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 10^{2} ning kvadrat ildizini chiqarish.

$$\frac{240}{35+25i\sqrt{3}+i\times 10\sqrt{3}}$$

35i\sqrt{3} ni olish uchun 25i\sqrt{3} va 10i\sqrt{3} ni birlashtirish.

$$\frac{240}{35+35i\sqrt{3}}$$

\frac{240}{35+35i\sqrt{3}} maxrajini 35-35i\sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{240\left(35-35i\sqrt{3}\right)}{\left(35+35i\sqrt{3}\right)\left(35-35i\sqrt{3}\right)}$$

Hisoblang: \left(35+35i\sqrt{3}\right)\left(35-35i\sqrt{3}\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{240\left(35-35i\sqrt{3}\right)}{35^{2}-\left(35i\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini 35 ga hisoblang va 1225 ni qiymatni oling.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(35i\sqrt{3}\right)^{2}}$$

\left(35i\sqrt{3}\right)^{2} ni kengaytirish.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(35i\right)^{2}\left(\sqrt{3}\right)^{2}}$$

2 daraja ko‘rsatkichini 35i ga hisoblang va -1225 ni qiymatni oling.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(-1225\left(\sqrt{3}\right)^{2}\right)}$$

\sqrt{3} kvadrati – 3.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(-1225\times 3\right)}$$

-3675 hosil qilish uchun -1225 va 3 ni ko'paytirish.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225-\left(-3675\right)}$$

3675 hosil qilish uchun -1 va -3675 ni ko'paytirish.

$$\frac{240\left(35-35i\sqrt{3}\right)}{1225+3675}$$

4900 olish uchun 1225 va 3675'ni qo'shing.

$$\frac{240\left(35-35i\sqrt{3}\right)}{4900}$$

\frac{12}{245}\left(35-35i\sqrt{3}\right) ni olish uchun 240\left(35-35i\sqrt{3}\right) ni 4900 ga bo‘ling.

$$\frac{12}{245}\left(35-35i\sqrt{3}\right)$$

\frac{12}{245} ga 35-35i\sqrt{3} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{12}{245}\times 35+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

\frac{12}{245}\times 35 ni yagona kasrga aylantiring.

$$\frac{12\times 35}{245}+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

420 hosil qilish uchun 12 va 35 ni ko'paytirish.

$$\frac{420}{245}+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

\frac{420}{245} ulushini 35 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{12}{7}+\frac{12}{245}\times \left(-35i\right)\sqrt{3}$$

-\frac{12}{7}i hosil qilish uchun \frac{12}{245} va -35i ni ko'paytirish.

$$\frac{12}{7}-\frac{12}{7}i\sqrt{3}$$

Ashyoviy qism

$$240Re(\frac{1}{35\left(1+\sqrt{3}i\right)})$$