SOLUTION: Find the principal argument Arg z for the ff values of z. (-1-i√3)^2

Question 1177967: Find the principal argument Arg z for the ff values of z.
(-1-i√3)^2
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

=> In your case

and => and

To find argument we use the following formula:

° if

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°

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Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The purely algebraic solution shown by the other tutor is fine, because the problem uses "nice" numbers.

deMoivre's Theorem gives us a tool for solving problems like this if the numbers aren't so nice.

(1) Represent the given number in polar form (I'll use degrees).

(-1,-i*sqrt(3)) = (2,240)

(2) deMoivre's Theorem says to square a complex number in polar form you square the magnitude and double the angle.

((-1,-i*sqrt(3))^2 = (2^2,2*240) = (4,480) = (4,120)

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.

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