Real part

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In mathematics, the real part of a complex number , is the first element of the ordered pair of real numbers representing , i.e. if , or equivalently, , then the real part of is . It is denoted by or . The complex function which maps to the real part of is not holomorphic.

In terms of the complex conjugate, the real part of is equal to .

For a complex number in polar form, , or equivalently, , it follows from Euler's formula that , and hence that the real part of is .

Sometimes computations with real periodic functions such as alternating currents and electromagnetic fields are simplified by writing them as the real parts of complex functions. See for example electrical impedance.

See also