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

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day! You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

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

Answers to Questions

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: $$ z = r \operatorname{e}^{i \theta} $$

Example: \( z = 1+i \) has for modulus \( \sqrt(2) \) and argument \( \pi/4 \) so its complex exponential form is \( z = \sqrt(2) e^{i\pi/4} \)

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: \( e^{i0} = e^{0} = 1 \) or \( e^{i\pi} = \cos(\pi) + i\sin(\pi) = -1 \)

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

Ask a new question

Source code

dCode retains ownership of the source code of the script Complex Number Exponential Form online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Complex Number Exponential Form script for offline use on PC, iPhone or Android, ask for price quote on contact page !