Mathematicians once turned up their noses at imaginary numbers. But complex analysis actually simplifies math and physics.

Solve \(\sqrt 3 \cos x + \sin x = \sqrt 2\), for \(0 \le x \le 2\pi\). First of all we need to put \(\sqrt 3 \cos x + \sin x\) into the form \(k\cos (x - \alpha ...

There are some trigonometric identities which you must remember in order to simplify trigonometric expressions when required. When you are asked to prove something, ignore the right hand side of ...