Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\sf \dfrac{(1 + \sqrt{3}\:i)^2 + \left(2\:cis\:\left(\dfrac{\pi }{12}\right)\right)^4}{6\:cis\:(\pi )}[/tex]
[tex]\sf \dfrac{(1 + \sqrt{3}\:i)^2 + \left(2\:.\:\left(cos\:\left(\dfrac{\pi }{12}\right) + i\:.\:sen\:\left(\dfrac{\pi }{12}\right)\right)\right)^4}{6\:.\:\left(cos\:(\pi ) + i\:.\:sen\:(\pi )\right)}[/tex]
[tex]\sf \dfrac{(1 + 2\sqrt{3}\:i + (\sqrt{3}\:i)^2) + \left(2^4\:.\:\left(cos\:\left(4\:.\:\dfrac{\pi }{12}\right) + i\:.\:sen\:\left(4\:.\:\dfrac{\pi }{12}\right)\right)\right)}{6\:.\:\left(cos\:(\pi ) + i\:.\:sen\:(\pi )\right)}[/tex]
[tex]\sf \dfrac{(-2 + 2\sqrt{3}\:i) + \left(16\:.\:\left(cos\:\left(\dfrac{\pi }{3}\right) + i\:.\:sen\:\left(\dfrac{\pi }{3}\right)\right)\right)}{6\:.\:\left(cos\:(\pi ) + i\:.\:sen\:(\pi )\right)}[/tex]
[tex]\sf \dfrac{(-2 + 2\sqrt{3}\:i) + \left(16\:.\:\left(\dfrac{1}{2} + i\:.\:\dfrac{\sqrt{3}}{2}\right)\right)}{6\:.\:\left(-1 + i\:.\:0)}[/tex]
[tex]\sf \dfrac{(-2 + 2\sqrt{3}\:i) + (8 + 8\sqrt{3}\:i)}{-6}[/tex]
[tex]\sf \dfrac{6 + 10\sqrt{3}\:i}{-6}[/tex]
[tex]\boxed{\boxed{\sf -1 - \dfrac{5\sqrt{3}\:i}{3}}}[/tex]
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Resposta:
[tex]\textsf{Leia abaixo}[/tex]
Explicação passo a passo:
[tex]\sf \dfrac{(1 + \sqrt{3}\:i)^2 + \left(2\:cis\:\left(\dfrac{\pi }{12}\right)\right)^4}{6\:cis\:(\pi )}[/tex]
[tex]\sf \dfrac{(1 + \sqrt{3}\:i)^2 + \left(2\:.\:\left(cos\:\left(\dfrac{\pi }{12}\right) + i\:.\:sen\:\left(\dfrac{\pi }{12}\right)\right)\right)^4}{6\:.\:\left(cos\:(\pi ) + i\:.\:sen\:(\pi )\right)}[/tex]
[tex]\sf \dfrac{(1 + 2\sqrt{3}\:i + (\sqrt{3}\:i)^2) + \left(2^4\:.\:\left(cos\:\left(4\:.\:\dfrac{\pi }{12}\right) + i\:.\:sen\:\left(4\:.\:\dfrac{\pi }{12}\right)\right)\right)}{6\:.\:\left(cos\:(\pi ) + i\:.\:sen\:(\pi )\right)}[/tex]
[tex]\sf \dfrac{(-2 + 2\sqrt{3}\:i) + \left(16\:.\:\left(cos\:\left(\dfrac{\pi }{3}\right) + i\:.\:sen\:\left(\dfrac{\pi }{3}\right)\right)\right)}{6\:.\:\left(cos\:(\pi ) + i\:.\:sen\:(\pi )\right)}[/tex]
[tex]\sf \dfrac{(-2 + 2\sqrt{3}\:i) + \left(16\:.\:\left(\dfrac{1}{2} + i\:.\:\dfrac{\sqrt{3}}{2}\right)\right)}{6\:.\:\left(-1 + i\:.\:0)}[/tex]
[tex]\sf \dfrac{(-2 + 2\sqrt{3}\:i) + (8 + 8\sqrt{3}\:i)}{-6}[/tex]
[tex]\sf \dfrac{6 + 10\sqrt{3}\:i}{-6}[/tex]
[tex]\boxed{\boxed{\sf -1 - \dfrac{5\sqrt{3}\:i}{3}}}[/tex]