Решение комбинаторных задач (вложение)

1) $= \frac{i*2*(1-i)}{(1+i)(1-i)} = \frac{2(i- i^{2}) }{1- i^{2} } = \frac{2(i+1)}{2} = i+1$

2) = $\sqrt{2} ^{2} + 2 \sqrt{2} i \sqrt{3} + (i \sqrt{3} )^{2} = 2+2 \sqrt{6} -3 = -1 +2 \sqrt{6}$

3) $= i(1-i^{23} ) = i(1-i ) = i- i^{2} = i-(-1) = i+1$

4) $= (3+5i)(7-2i) = 21-6i+35i-10 i^{2} = 21+29i+10 = 31+29i$

5) $= 19+6i-7+3i = 12+9i$