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In terms of the Complex Conjugate \bar{z}, the real part of z is equal to z+\bar z\over2.

For a complex number in Polar Form , z = (r, heta ), or equivalently, z = r(cos heta + i \sin heta) , it follows from Euler's Formula that z = re^{i heta}, and hence that the real part of re^{i heta} is r\cos heta.

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 .


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