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Complex Number Exponential Form

Tool for converting complex numbers into exponential notation and vice versa by calculating the values of the module and the main argument of the complex number.

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Complex Number Exponential Form -

Tag(s) : Mathematics

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# Complex Number Exponential Form

## Complex Number Converter

### From modulus and argument

Tool for converting complex numbers into exponential notation and vice versa by calculating the values of the module and the main argument of the complex number.

### What is the exponential form of a complex number?

The exponential notation of a complex number $$z$$ of argument $$\ theta$$ and of modulus $$r$$ is: $$z = r \operatorname{e}^{i \theta}$$

dCode offers a complex number modulus calculator and a complex number argument calculator tools.

### What is Euler's formula?

Euler's formula applied to a complex number connects the cosine and the sine with complex exponential notation: $$e^{i\theta } = \cos {\theta} + i \sin {\theta}$$ with $$\theta \in \mathbb{R}$$

### What are the properties of complex exponentiation?

If the complex number has no imaginary part: $$e^{i0} = e^{0} = 1$$ ot $$e^{i\pi} = \cos(\pi) + i\sin(\pi) = -1$$

If the complex number has no real part: $$e^{i(\pi/2)} = \cos{\pi/2} + i\sin{\pi/2} = i$$ or $$e^{i(-\pi/2)} = \cos{-\pi/2} + i\sin{-\pi/2} = -i$$