Real part

In mathematics, the real part of a complex number z, is the first element of the ordered pair of real numbers representing z, i.e. if z = (x, y) , or equivalently, z = x+iy, then the real part of z is x. It is denoted by mbox{Re}z or Re z. The complex function which maps z to the real part of z is not holomorphic.

Related Topics:
Mathematics - Complex number - Ordered pair - Real numbers - Complex function - Holomorphic

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In terms of the complex conjugatear{z}, the real part of z is equal to z+ar zover2.

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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 rcos heta.

Related Topics:
Polar form - Euler's formula

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