Question

ну умные люди : ) (если можно, то распишите ) (7-i/3+i)^2

Answer 1

$( 7 - i/3 + i )^2 = ( 7 - \frac{i}{3} + i )^2 = ( 7 - \frac{i}{3} + \frac{3i}{3} )^2 = ( 7 + \frac{3i}{3} - \frac{i}{3} )^2 = \\\\ = ( 7 + \frac{3i-i}{3} )^2 = ( 7 + \frac{2i}{3} )^2 = 7^2 + 2 \cdot 7 \cdot \frac{2}{3} i + ( \frac{2}{3} i) ^2 = \\\\ = 49 + \frac{ 2 \cdot 7 \cdot 2 }{3} i + \frac{2^2}{3^2} i^2 = 49 + \frac{ 2^2 \cdot 7 }{3} i + \frac{4}{9} \cdot (-1) = 49 + \frac{ 4 \cdot 7 }{3} i - \frac{4}{9} = \\\\ = 48 + \frac{9}{9} - \frac{4}{9} + \frac{28}{3} i = 48 + \frac{9-4}{9} + \frac{ 27 + 1 }{3} i = 48 + \frac{5}{9} + ( 9 + \frac{1}{3} ) i \ ;$

О т в е т :   $( 7 - i/3 + i )^2 = 48 \frac{5}{9} + 9 \frac{1}{3} i \ ;$