Question 1208325
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Answer: <font color=red>False</font>


Explanation


Let's look at a counterexample. Consider the cube roots of 16.
We wish to solve z^3 = 16 or z^3-16 = 0.
According to the <a href="https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/06%3A_The_Polar_System/6.05%3A_De_Moivre's_and_the_nth_Root_Theorem">Nth Root Theorem</a> we find the 3 cube roots are
S = 16^(1/3)*cis(0)
P = 16^(1/3)*cis(120)
A = 16^(1/3)*cis(240)
where cis(x) = cos(x)+i*sin(x) and the angle mode is in degrees.
If you want to convert to radians, then,
120 degrees = 2pi/3 radians
240 degrees = 4pi/3 radians
The order of the cube roots doesn't matter. Try out different permutations to see why. 


Arg(S)+Arg(P) = 2*Arg(A)
0+120 = 2*240
120 = 480
Reaching a false statement proves that the original equation is <font color=red>false</font>.


A bit of extra info:
Notice how angles 120 and 480 are coterminal. This is because 120+360=480. 
If you were to involve mod 360 then the two sides would agree on the same number and the equation would be true. 
To learn more, search "modular arithmetic".
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