Euler's Formula

Euler’s Formula states that for any real number \( x \), the equation \( e^{ix} = \cos(x) + i\sin(x) \) holds true, where \( e \) is a mathematical constant approximately equal to 2.718, \( i \) is the imaginary unit (the square root of -1), and \( \cos \) and \( \sin \) are familiar trigonometric functions. This formula elegantly connects complex exponential functions with trigonometry, illustrating the relationship between algebra and geometry. It is a cornerstone in mathematics and physics, especially in fields dealing with waves and oscillations.