NoblePenguin
NoblePenguin NoblePenguin
  • 01-04-2021
  • Mathematics
contestada

Please find the square roots of the following complex number.

[tex]z = 81(\cos(\frac{4\pi}{9})+i\sin(\frac{4\pi}{9}))[/tex]

Respuesta :

Wolfyy
Wolfyy Wolfyy
  • 01-04-2021

Hey there,

First, find the square root of the given equation.

[tex]\sqrt{z}=\sqrt{81(\text{cos}(\frac{4\pi}{9})+i\text{sin}(\frac{4\pi}{9})}\\=9\text{cos}\frac{1}{2}(2k\pi+(\frac{4\pi}{9}))+i\text{sin}\frac{1}{2} (2k\pi+(\frac{4\pi}{9}))[/tex]

Keep in mind that this is solved for k = 0 and 1.

Second, simplify.

[tex]=9\text{cos}(\frac{2\pi}{9})+i\text{sin}(\frac{2\pi}{9})~\text{or}~9\text{cos}(\frac{11\pi}{9})+i\text{sin}(\frac{11\pi}{9})[/tex]

Best of Luck!

Answer Link

Otras preguntas

Do cows have toes? (Yes or No)
What is the slope of the line that passes through the points (-4, -8) and (-8,-6)?
In the next five years, from which source do you think most people will purchase a GPS? Why?
What are ways that people want to “progress” the US today?
48. A chemist takes a liquid at 10.4°C and cools it until its temperature is -1.5°C. Find the change in temperature.
Juanita walked 4 miles on a park trail in 1 1/3 hours. What was her average speed in miles per hour?
A food processing plant is packaging 32oz bags of coffee beans. The tolerance is 0.25 ounces. 100 bags of coffee were weighed, and the number at each weight is
Caring for the children?A. ManB. Woman C. Both​
how arev u guys doing
Which of the following ratios is equivalent to 2:3 A. 12.13 B. 14.21 C. 20.25 D. 1.4