Reciprocal of a complex number
Online calculator for calculating the reciprocal value (inverse) of a complex number
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'.
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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
\(z = Re(3)+Im(5)\)
\(\displaystyle\frac{1}{z}=\frac{3}{3^2+5^2}+\frac{-5}{3^2+5^2}\)
\(\displaystyle\frac{1}{z}=\frac{3}{9+25}+\frac{-5}{9+25}\)
\(\displaystyle\frac{1}{z}=\frac{3}{34}+\frac{-5}{34}\)
\(\displaystyle\frac{1}{z}= 0.088-0.147i\)
More complex functions
Absolute value (abs) • Angle • Conjugate • Division • Exponent • Logarithm to base 10 • Multiplication • Natural logarithm • Polarform • Power • Root • Reciprocal • Square root •Cosh • Sinh • Tanh •
Acos • Asin • Atan • Cos • Sin • Tan •
Airy function • Derivative Airy function •
Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye •
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