Euler’s identity shows a deep connection between exponential functions and trigonometry. It states that raising the number e to an imaginary power gives a combination of cosine and sine. This elegant formula links algebra, geometry, and complex numbers, and is widely used in physics, engineering, and signal processing. تُظهر معادلة أويلر علاقة عميقة بين الدوال الأسية والدوال المثلثية. تنص على أن رفع العدد e إلى قوة تخيلية يعطي مزيجاً من جيب التمام وجيب الزاوية. تُعد هذه الصيغة الأنيقة رابطاً بين

📌Euler's formula is a fundamental equation in complex analysis that shows a deep connection between exponential functions and trigonometric functions. It states that *e* raised to the power of *i* times *x* equals the cosine of *x* plus *i* times the sine of *x*. In simple terms, it expresses how complex exponentials can represent circular motion. This formula is widely used in engineering, physics, and mathematics because it elegantly links exponential growth, rotation, and wave behavior in a