Reciprocal of a complex number

Calculator and formulas for reciprocal (inverse) of a complex number

Reciprocal value calculator


This function calculates the reciprocal of a complex number.

To perform the calculation, enter the value of the complex number whose reciprocal is to be calculated. Then click the button 'Calculate'.


Reciprocal value calculator

 Input
Complex number +  i
Decimal places
 Results
Reciprocal

Formula for reciprocal value

In the following description, \(z\) stands for the complex number. \(x\) stands for the real value \(Re\) and \(y\) for the imaginary value \(Im\).

\(z = Re(x)+Im(y)\)
\(\displaystyle\frac{1}{z}=\frac{x}{x^2+y^2}+\frac{-y}{x^2+y^2}\)

Example

\(z = Re(3)+Im(5)\)
\(\displaystyle\frac{1}{z}=\frac{3}{3^2+5^2}+\frac{-5}{3^2+5^2}\)
\(\displaystyle\frac{1}{z}=\frac{3}{9+25}+\frac{-5}{9+25}\)
\(\displaystyle\frac{1}{z}=\frac{3}{34}+\frac{-5}{34}\)
\(\displaystyle\frac{1}{z}= 0.088-0.147i\)
Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?