Conjugate complex numbers
Calculator and formula for conjugating complex numbers
The calculator on this page conjugates a complex number. To calculate, enter a complex number and then click the Calculate button.
The result is displayed as a complex number.
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Conjugate a complex number
Every complex number has a so-called complex conjugate number. These conjugate complex numbers are needed in the division, but also in other functions.
As an example we take the number \(5+3i\) . The complex number conjugated to \(5+3i\) is \(5-3i\). The real parts of the two numbers are the same, the imaginary parts of the two differ only by the sign.
Let's take a look at the product of the two numbers
\((5+3i)ยท(5-3i) = 25-15i + 15i-9i = 25+9 = 34\)
The product of the complex numbers and their conjugates is real. This is a special property of conjugate complex numbers that will prove useful.
For the conjugate complex number \(a-bi\) schreibt man \(\overline{z}=a-bi\).
So in the example above \(\overline{5+3i}=5-3i\)
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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