calculer-1-2-i-3-2-3-

Question Number 176049 by doline last updated on 11/Sep/22

c a l c u l e r (- 1 / 2 + i \sqrt{{3 / 2)}^{3}}

Answered by Rasheed.Sindhi last updated on 11/Sep/22

- 1 / 2 + i \sqrt{{3 / 2)}^{3}}

= - \frac{1}{2} + i {(\sqrt{3 / 2})}^{3}

= - \frac{1}{2} + i {(\sqrt{3 / 2})}^{2} (\sqrt{3 / 2})

= - \frac{1}{2} + \frac{3 i}{2} \cdot \frac{\sqrt{3}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}

= - \frac{1}{2} + \frac{3 i}{2} \cdot \frac{\sqrt{6}}{2}

= - \frac{1}{2} + \frac{3 i \sqrt{6}}{4} = \frac{- 2 + 3 i \sqrt{6}}{4}