In NUS, department of mathematics, QE in semester 1 AY 08-09 has the following complex trigonometric equation
To solve the above equation, firstly we can see that . Then the given equation can be transformed to . Using the following formulas
we get the following equivalent equation
i.e., . Denoting one can easily compute that . Thus, the solutions are
where . If you wish to express the solutions in Cartesian form, then
where is the answer.