Whakaoti i te frac{isqrt{2}-5}{i+sqrt{2}}

$$\frac { i \sqrt { 2 } - 5 } { i + \sqrt { 2 } }$$

Aromātai

$$-\frac{4\sqrt{2}}{3}+\frac{7}{3}i\approx -1.885618083+2.333333333i$$

Ngā Upane Otinga

Whakangāwaritia te tauraro o \frac{i\sqrt{2}-5}{i+\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te i-\sqrt{2}.

$$\frac{\left(i\sqrt{2}-5\right)\left(i-\sqrt{2}\right)}{\left(i+\sqrt{2}\right)\left(i-\sqrt{2}\right)}$$

Whakaarohia te \left(i+\sqrt{2}\right)\left(i-\sqrt{2}\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}.

$$\frac{\left(i\sqrt{2}-5\right)\left(i-\sqrt{2}\right)}{i^{2}-\left(\sqrt{2}\right)^{2}}$$

Pūrua i. Pūrua \sqrt{2}.

$$\frac{\left(i\sqrt{2}-5\right)\left(i-\sqrt{2}\right)}{-1-2}$$

Tangohia te 2 i te -1, ka -3.

$$\frac{\left(i\sqrt{2}-5\right)\left(i-\sqrt{2}\right)}{-3}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o i\sqrt{2}-5 ki ia tau o i-\sqrt{2}.

$$\frac{-\sqrt{2}-i\left(\sqrt{2}\right)^{2}-5i+5\sqrt{2}}{-3}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{-\sqrt{2}-i\times 2-5i+5\sqrt{2}}{-3}$$

Whakareatia te -i ki te 2, ka -2i.

$$\frac{-\sqrt{2}-2i-5i+5\sqrt{2}}{-3}$$

Tangohia te 5i i te -2i, ka -7i.

$$\frac{-\sqrt{2}-7i+5\sqrt{2}}{-3}$$

Pahekotia te -\sqrt{2} me 5\sqrt{2}, ka 4\sqrt{2}.

$$\frac{4\sqrt{2}-7i}{-3}$$

Me whakarea tahi te taurunga me te tauraro ki te -1.

$$\frac{-4\sqrt{2}+7i}{3}$$

Wāhi Tūturu

$$-\frac{4 \sqrt{2}}{3} = -1.885618083164127$$