Euler's Theorem, also known as Euler's formula, is a mathematical theorem that relates the trigonometric functions of a complex number. It states that for any complex number z, e^(iz) = cos(z) + i*sin(z), where e is Euler's number and i is the imaginary unit.
Euler's Theorem was discovered by the famous Swiss mathematician, Leonhard Euler, in the 18th century. He is also known for his contributions in various fields of mathematics, including calculus, number theory, and graph theory.
Euler's Theorem is significant because it provides a link between two fundamental mathematical concepts - complex numbers and trigonometry. It is also used in various applications, such as in electrical engineering, signal processing, and physics.
Euler's Theorem has various applications in mathematics and other fields. It is used in solving problems involving complex numbers, calculating Fourier series, and understanding the behavior of alternating currents in electrical circuits. It also has applications in quantum mechanics and signal processing.
Euler's Theorem and Euler's Identity are closely related but not the same. Euler's Identity is a special case of Euler's Theorem, where z is equal to π. This results in e^(iπ) = cos(π) + i*sin(π) = -1 + 0i = -1. Euler's Identity is often considered more elegant and significant, as it links five fundamental mathematical constants - 0, 1, e, π, and i - in one equation.