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.
Complex Number Exponential Form - dCode
Tag(s) : Arithmetics, Geometry
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!
Complex Number Exponential Form
Sponsored ads
Complex Number Converter
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 \( z = \sqrt(2) e^{i\pi/4} \)
dCode offers a complex modulus calculator and a complex 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: \( e^{i0} = e^{0} = 1 \) 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. So if you need to download the online Complex Number Exponential Form script for offline use, check contact page !
Questions / Comments
