SOLUTION: Find the cube roots of 2 + i 2 . Locate them graphically

Question 302205: Find the cube roots of 2 + i 2 . Locate them graphically
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the cube roots of 2 + i 2 . Locate them graphically
z = sqrt(8)cis(45)
z^(1/3) = (8^(1/6))cis(15)
= sqrt(2)cis(15)
= sqrt(2)[cos(15,135,255) + isin(15,135,255)]
---------------------
You can use the half-angle formulas to eliminate the sine and cosine.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the cube roots of 2 + i 2 . Locate them graphically
-----------------------
Plot the point (2,2) so you can see what is happening.
-----
Convert to trip form:
r = sqrt(2^2 + 2^2)= 2sqrt(2) = 8^(1/2)
theta = tan^-1(2/2) = 45 degrees + 360n
-----------
(2+2i)^(1/3) = (8)^(1/6)cis[(45+360n)/3] for n = 0,1,2
---
If n = 0 ; 8^(1/6)cis(15)
If n = 1 ; 8^(1/6)cis(135)
If n = 2 ; 8^(1/6)cis(255)
----
Graphically these are three points on a circle centered
at the origin with radius = 8^(1/6).
The points are located at 15 degrees, 135 degrees, and 255 degrees
===================================================================
Cheers,
Stan H.
================
RELATED QUESTIONS
Find the cube roots of... (answered by Edwin McCravy)
Please tell how to graphically locate the nth roots of a complex number, given the... (answered by KMST)
How do I find the area of this triangle: {{{drawing(400,350,-1,3,-1,2.5,... (answered by Edwin McCravy)
determine all the indicated roots and represent them graphically : a)... (answered by greenestamps)
Find the 3 cube roots of -i in polar... (answered by robertb)
7. Find the cube roots of... (answered by Fombitz)
Find the 3 cube roots of i in polar... (answered by ikleyn,Edwin McCravy)
Find the cube roots of... (answered by solver91311)
how can i locate the square roots of different numbers in the number... (answered by solver91311)