Question

Rezolvati :
[tex](- \frac{1}{2} + i\frac{ \sqrt{3} }{2} )^{3} + (-\frac{1}{2} - i\frac{ \sqrt{3} }{2} )^{3}
[/tex] = ?

Answer 1

$=(- \frac{1}{2})^{3} +3*(- \frac{1}{2})^{2}*i \frac{ \sqrt{3} }{2} +3*(- \frac{1}{2} )* (i \frac{ \sqrt{3}}{2}) ^{2} + (i \frac{ \sqrt{3} }{2}) ^{3} + \\ +(- \frac{1}{2})^{3}-3*(- \frac{1}{2})^{2}*i \frac{ \sqrt{3} }{2}+3*(- \frac{1}{2} )* (i \frac{ \sqrt{3}}{2}) ^{2}- (i \frac{ \sqrt{3} }{2})= \\ =2(- \frac{1}{2})^{3}+6*(- \frac{1}{2} )* (i \frac{ \sqrt{3}}{2}) ^{2} =- \frac{2}{8} -3*(- \frac{3}{4} )= \\ =- \frac{1}{4} + \frac{9}{4} = \frac{8}{4} =2$