Given z1=e^(iπ/4) and z2=e^(−iπ/3) , find the arguments of (z1^3/z2).

Question

The answer in the book is −11π/12.

Please show step by step.

Answer 1

z₁³ / z₂ = (e^iπ/4)³ / e^-iπ/3 = e^3iπ/4 e^iπ/3 = e^iπ13/12

 

The argument is 13π/12, measured from the +x axis in a counter clockwise sense.  However, that is equivalent to 11π/12 measured from the +x axis in a clockwise sense, which would be an argument of -11π/12.