On Khan academy their is this question asking:
Find the solution of the equation whose argument is between 180 and 270 degrees, z^5 = -243i
Now their is also a document on the khan academy site that says if their is a negative in the equation, such as the -243i part, that the argument will be 5(theta) = 180 + k(360)... And if their is no negative then the argument will be 5(theta) = 90 + k(360)... However when I click to get a hint for the question it says that the argument is 5(theta) = 270 + k(360). This is really confusing me because on a similar question that asks for the solution whose argument is between 225 degrees and 315 degrees, when I ask for a hint, they tell me the argument is 5(theta) = 90 + k(360).
Can someone explain how they came to the argument of 270?