queenkennedy01
queenkennedy01 queenkennedy01
  • 25-05-2018
  • Mathematics
contestada

use demovires theorem to write the complex number in trigonometric form.
[tex] (\sqrt{3} + i)^{3} [/tex]

Respuesta :

LammettHash
LammettHash LammettHash
  • 25-05-2018
[tex]\sqrt3+i=2\left(\dfrac{\sqrt3}2+\dfrac12i\right)[/tex]

[tex]\begin{cases}\cos\dfrac\pi6=\dfrac{\sqrt3}2\\\\\sin\dfrac\pi6=\dfrac12\end{cases}[/tex]

[tex]\implies\sqrt3+i=2e^{i\pi/6}[/tex]

By DeMoivre's theorem,

[tex](\sqrt3+i)^3=(2e^{i\pi/6})^3=8e^{i\pi/2}=8\left(\cos\dfrac\pi2+i\sin\dfrac\pi2\right)=8i[/tex]
Answer Link

Otras preguntas

A triangle has sides 42, 4x, and 2x−6. What is the possible range of x? ? < x < ?
Help me out you guys please
What are two Amphibian behaviors
The framers were dedicated to the concept of limited government. they were convinced:
During a laboratory investigation, biology students were asked to classify organisms on prepared slides as either eukaryotes or prokaryotes. Which of the follow
Give the name of the watershed in austin that contains the most wells. how many wells does it contain
How does the reader know vera is pleased with the tale she told Frampton? a. she stares out the window in surprise and horror b. she makes him turn to look out
What did winston churchill mean by this? "But if we fail, then the whole world, including the United States, including all that we have known and cared for, wil
Read the sentence. Georgia O’Keeffe was a great artist who created paintings of New Mexico desert scenes. Which is the underlined clause? A. an independent cl
In western culture, sadness at funerals and happiness at weddings are examples of