Euler's formula

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In complex analysis, Euler's formula, also sometimes called Euler's relation, is an equation involving complex numbers and trigonometric functions. More specifically, it states that

where x is a real number, e is Euler's number and i is the imaginary unit.

It makes a relation between trigonometric functions and exponential functions of complex numbers. It is named after Leonhard Euler, who published it in 1748. When he published it, Euler said that the angle must be a real number. Later, it turned out that the formula also works if the angle is not a real number, but a complex one.

When the angle is  and , Euler's formula becomes   and , respectively.

 Related pages 

 Euler's identity

 References 

Category:Complex analysis
Category:Trigonometry