Complex Variables - principal argument

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The discussion focuses on finding the principal argument of the complex number z = (sqrt(3) - i)^6. The initial confusion arises from attempting to relate the expression to the exponential form exp(i*theta*6) and determining the correct theta. The user realizes that while sin(theta) and cos(theta) must satisfy specific conditions, they are not aligning correctly with the values derived from the original expression. Ultimately, the user indicates a resolution to their understanding of the problem. The thread highlights the common challenges faced when dealing with complex variables and their arguments.
YoshiMoshi
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Homework Statement



Find the principle argument Arg z when

z = (sqrt(3) - i)^6

Homework Equations

The Attempt at a Solution



I'm sorry to say that I'm not sure how to solve this problem. It's my understanding that what this question is basically asking me to do is find theta such that

exp(i*theta*6) = (sqrt(3)-i)^6

However I'm not sure how to solve this.

cos(theta) = sqrt(3)
sin(theta) = -i

In order for sin(theta) = -1, then theta must be equal to -pi/2. However cos(-pi/2) =/= sqrt(3). I seem to not understand what this question is asking me exactly or how to solve this problem.

Thanks for any help.
 
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Never mind. I understand how to do it now.
 

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