Question

Выручайте
Выполнить действия:

1) i+i^33

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

3) i^17+i(1-i)

Answer 1

1)
$i + {i}^{33} = i + {i}^{32 + 1} = \\ = i + {i}^{32} \times {i}^{1} = \\ = i + 1i = i + i = \\ = 2i$
2)
$\frac{5i}{ \sqrt{2} - i \sqrt{3} } = \frac{5i}{ \sqrt{2} - \sqrt{3}i } = \\ = i( \sqrt{2} + \sqrt{3} i) = \\ = \sqrt{2} i + {i}^{2} \sqrt{3} = \\ = \sqrt{2} i + 1 \sqrt{3} = \\ = \sqrt{2} i + \sqrt{3}$

3)
${i}^{16 + 1} + i - {i}^{2} = \\ = {i}^{16} \times {i}^{1} + i - ( - 1)= \\ = 1i + i + 1 = \\ = i + i + 1 = \\ = 2i + 1$