Liczby zespolone - oblicz -sprawdzenie

[doshka]

\(\displaystyle{ 1. \frac{( \sqrt{2} + \sqrt{7}i) ( \sqrt{2} - \sqrt{7}i)}{ (1+i)^{3}}}\)

\(\displaystyle{ 2. (1+2i)^{3}}\)


co do pierwszego:

\(\displaystyle{ 1. \frac{( \sqrt{2} + \sqrt{7}i) ( \sqrt{2} - \sqrt{7}i)}{ (1+i)^{3}}= \frac{2+7}{1+3i-3-i}= \frac{9}{-2 + 2i} = \frac{9 (-2-2i)}{(-2+2i)(-2-2i)} = \frac{-18-18i}{4+4} = \frac{9 - 9i}{4} hmm ???}\)

\(\displaystyle{ 2. (1+2i)^{3}= 1 - 12 +6i - 8i = -11 - 2i ?}\)

[soku11]

1.
\(\displaystyle{ ...=\frac{-18-18i}{4+4}=\frac{-9i-9}{4}}\)

2. jest ok.

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