Question 466466: Find all complex roots. Leave your answers in polar form with the argument in degrees.
The complex fourth roots of -9 i.
The answer will be submitted as the following:
z(subscript)k=[cos(__ degrees+__degrees k) + i sin (__degrees+__degrees k)], k=0,1,...,__
(Type the exact answer in the first answer box. Type any angles in degrees between 0 degrees and 360 degrees. Type all degree measures rounded to one decimal place as needed.)
-------------------
*If possible, explain each step of this process, I have went through my book and also all over the internet, and have not found any guidelines to use for a negative # with an i.
Thank you for any help you can offer. I am really bad at math, and do not understand this lesson.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The complex fourth roots of -9 i.
---
The number is 0-9i
----
Polar Form:
r = sqrt(0^2 + 9^2) = 9
--
theta = -9/0 is undefined
theta = 270 + 360k degrees where k = 0,1,2,3...
----------------------------
4th root = 9^(1/4)[cos(270 +360k)/4 + isin(270+260k)/4] where k = 0,1,2,3
----
If k = 0 you get 9^(1/4)(cos(270/4) + isin(270/4))
---
If k = 1 you get 9^(1/4)(cos((270/4)+90) + isin((270/4)+90))
---
If k = 2 you get 9^(1/4)(cos((270/4)+2*90)+ isin((270/4)+2*90))
---
If k = 3 you get 9^(1/4)(cos((270/4)+3*90)+isin((270/4)+3*90))
=================================================================
Cheers,
Stan H.
|
|
|
