SOLUTION: how do you find the square root of 25/3 using complex numbers?

Question 238734: how do you find the square root of 25/3 using complex numbers?
Found 2 solutions by checkley77, stanbon:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
sqrt25/3=5sqrt(1/3)=5(1/1.732)=5/1.732=2.8868 ans.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
how do you find the square root of 25/3 using complex numbers?
-----------------
25/3 = 25/3 + 0i
---------------------
Trigonometric Form:
25/3+0i = (25/3)(cos(0)+isin(0))
-------------------------------
To take the square root:
(25/3)^(1/2) = (25/3)^1/2(cos[(0+2npi)/2] + isin([0+2npi)/2] for n = 0,1
---------------------
For n=0 you get:
(25/3)^(1/2)(cos(0) + isin(0) = sqrt(25/3) + 0i
------------------------------
For n=1 you get:
(25/3)^(1/2)(cos(pi)+isin(pi)) = -sqrt(25/3)+0i
=====================================================
That is the complex number answer but I think you really
may have wanted the irrational number answer which is
as follows:
---
sqrt(25/3) = 5sqrt(1/3) = 5sqrt(3/9) = 5sqrt(3)/3
= (5/3)sqrt(3)
=====================================================
Cheers,
Stan H.
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