Question

Выручайте
Выполнить действия:

1) i+i^33

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

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