Przedstawić w postaci algebraicznej liczby:
1) \(\displaystyle{ \frac{2}{i}+ \frac{3}{1+i}= \frac{2(1+i)+3i}{i+ i^{2} } = \frac{2+5i}{i-1}= \frac{(2+5i)(i+1)}{i ^{2}-1 }= \frac{-3+7i}{-2} = \frac{3}{2} - \frac{7}{2}i}\)
2)\(\displaystyle{ ( \frac{3+4i}{3-4i}- \frac{3-4i}{3+4i} )^{3}=( \frac{(3+4i)^{2}-(3-4i)^{2}}{9+16} )^{3}=( \frac{48}{25}i )^{3}=- \frac{48^{3}}{25^{3}}i}\)
3)\(\displaystyle{ \frac{Im((1+i)(4-3i)) }{3-4i}= \frac{Im(4-3i+4i+3}{3-4i}= \frac{1}{3-4i}= \frac{3+4i}{25}= \frac{3}{25}+ \frac{4}{25}i}\)
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