<PRE><B>Question 445902</B>
Find the three cube roots of Z = 5cos225degrees + jsin 225degrees and show these on an argand diagram
Which of these roots is the PRINCIPAL ROOT?
-----------------------------------------------
Z^(1/3)  = 5^(1/3)[cos(225+360n)/3 + jsin(225+360n)]
--------------------
Let n = 0 then z^(1/3) = 5^(1/3)[cos(75) + jsin(75)]
That is the principal root
-----------------
Let n = 1 then z^(1/3) = 5^(1/3)[cos(195) + jsin(195)]
--------
Let n = 2 then z^(1/3) = 5^(1/3)[cos(315) + jsin(315)]
===============
Those are the 3 cube roots.
===============
Cheers,
Stan H.

 </PRE>