Question 1177967
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The purely algebraic solution shown by the other tutor is fine, because the problem uses "nice" numbers.<br>
deMoivre's Theorem gives us a tool for solving problems like this if the numbers aren't so nice.<br>
(1) Represent the given number in polar form (I'll use degrees).<br>
(-1,-i*sqrt(3)) = (2,240)<br>
(2) deMoivre's Theorem says to square a complex number in polar form you square the magnitude and double the angle.<br>
((-1,-i*sqrt(3))^2 = (2^2,2*240) = (4,480) = (4,120)<br>
The problem only asked for the principal argument for the given expression, so you wouldn't be concerned with the magnitude.  You would only have to know that the angle for (-1-i*sqrt(3)) is 240 degrees, so the angle for that number squared is 480 degrees, or 120 degrees.<br>