Whakaoti i te sqrt{-2}+9sqrt{-8}-4sqrt{-16}

$$\sqrt { - 2 } + 9 \sqrt { - 8 } - 4 \sqrt { - 16 }$$

Aromātai (complex solution)

$$19\sqrt{2}i-16i\approx 10.870057685i$$

Ngā Upane Otinga

Tauwehea te -2=2\left(-1\right). Tuhia anō te pūtake rua o te hua \sqrt{2\left(-1\right)} hei hua o ngā pūtake rua \sqrt{2}\sqrt{-1}. Hei tōna tikanga, ko te pūtake rua o -1 ko i.

$$\sqrt{2}i+9\sqrt{-8}-4\sqrt{-16}$$

Tauwehea te -8=\left(2i\right)^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{\left(2i\right)^{2}\times 2} hei hua o ngā pūtake rua \sqrt{\left(2i\right)^{2}}\sqrt{2}. Tuhia te pūtakerua o te \left(2i\right)^{2}.

$$\sqrt{2}i+9\times \left(2i\right)\sqrt{2}-4\sqrt{-16}$$

Whakareatia te 9 ki te 2i, ka 18i.

$$\sqrt{2}i+18i\sqrt{2}-4\sqrt{-16}$$

Pahekotia te \sqrt{2}i me 18i\sqrt{2}, ka 19i\sqrt{2}.

$$19i\sqrt{2}-4\sqrt{-16}$$

Tātaitia te pūtakerua o -16 kia tae ki 4i.

$$19i\sqrt{2}-4\times \left(4i\right)$$

Whakareatia te -4 ki te 4i, ka -16i.

$$19i\sqrt{2}-16i$$

Wāhi Tūturu (complex solution)

$$0$$

Aromātai

$$\text{Indeterminate}$$