Răspuns:
[tex]z = \frac{2 + 3i}{(1 + i) {}^{10} } = \frac{2 + 3i}{((1 + i) {}^{2}) {}^{5} } = \frac{2 + 3i}{(1 + 2i + {i}^{2} ) {}^{5} } [/tex]
[tex] = \frac{2 + 3i}{(2i) {}^{5} } = \frac{2 + 3i}{32i} = \frac{3}{36} - \frac{1}{16} i[/tex]
[tex] |z| = \sqrt{( \frac{3}{36} ) {}^{2} + ( - \frac { 1}{16}) {}^{2} } = \sqrt{ \frac{9}{1024} - \frac{1}{256} } = \sqrt{ \frac{13}{1024} } = \frac{ \sqrt{13} }{32} [/tex]
