Whakaoti i te 240/25+25sqrt{3i+10+sqrt{300}i}

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

Aromātai

$$\frac{48}{7\left(1+\sqrt{3}i\right)}\approx 1.714285714-2.969229956i$$

Ngā Upane Otinga

Tāpirihia te 25 ki te 10, ka 35.

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

Tauwehea te 300=10^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{10^{2}\times 3} hei hua o ngā pūtake rua \sqrt{10^{2}}\sqrt{3}. Tuhia te pūtakerua o te 10^{2}.

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

Pahekotia te 25i\sqrt{3} me 10i\sqrt{3}, ka 35i\sqrt{3}.

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

Whakangāwaritia te tauraro o \frac{240}{35+35i\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te 35-35i\sqrt{3}.

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

Whakaarohia te \left(35+35i\sqrt{3}\right)\left(35-35i\sqrt{3}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Tātaihia te 35 mā te pū o 2, kia riro ko 1225.

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

Whakarohaina te \left(35i\sqrt{3}\right)^{2}.

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

Tātaihia te 35i mā te pū o 2, kia riro ko -1225.

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

Ko te pūrua o \sqrt{3} ko 3.

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

Whakareatia te -1225 ki te 3, ka -3675.

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

Whakareatia te -1 ki te -3675, ka 3675.

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

Tāpirihia te 1225 ki te 3675, ka 4900.

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

Whakawehea te 240\left(35-35i\sqrt{3}\right) ki te 4900, kia riro ko \frac{12}{245}\left(35-35i\sqrt{3}\right).

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

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{12}{245} ki te 35-35i\sqrt{3}.

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

Tuhia te \frac{12}{245}\times 35 hei hautanga kotahi.

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

Whakareatia te 12 ki te 35, ka 420.

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

Whakahekea te hautanga \frac{420}{245} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 35.

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

Whakareatia te \frac{12}{245} ki te -35i, ka -\frac{12}{7}i.

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

Wāhi Tūturu

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