I've stuck on a basic exercise.
I must find all complex numbers such that .
Which is equivalent to say that .
I remember a long time ago I've learned a formula where , and , the module of were involved that could solve for an argument of . This is the only way that comes to my mind right now about how to solve the problem.
Sure! We're looking for complex numbers in the first quadrant of the complex plane that are along the line . Hence the real and imaginary parts must be equal and positive (due to the limitation of the first quadrant, because we have an argument of ).
This explain the first line of your post. To pass for the second line, divide by which is a positive number so there's no problem.
And now we must find such that , which happens only when , .
So the answer is , , .