Exponent of a complex number

Online calculator for calculating the exponent of a complex number

Calculate exponent of a complex number

The function returns e to the power specified by a complex number.

Exponent calculator

Complex number +  i
Decimal places

Formulas for calculating the exponent

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

\(z = Re(x) + Im(y)\)

\(\displaystyle e^z=e^x\cdot cos(y) +e^x\cdot sin(y)\)



\(\displaystyle e^z = e^3\cdot cos(5) +e^3\cdot sin(5)\)

\(\displaystyle e^z = 20.086\cdot 0.284 +20.086\cdot −0.959 = 5.698−19.261i\)
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