- Real part
In
mathematics , the real part of acomplex number , is the first element of theordered pair ofreal numbers representing , i.e. if , or equivalently, , then the real part of is . It is denoted by Re{"z"} or {"z"}, where is a capital R in the Fraktur typeface. Thecomplex function which maps to the real part of is notholomorphic .In terms of the
complex conjugate , the real part of is equal to .For a complex number in polar form, , the Cartesian (rectangular) coordinates are ,or equivalently, It follows from
Euler's formula that , and hence that the real part of is .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
Phasor (sine waves) )Similarly, trigonometry can often be simplified by representing the sinusoids in terms of the real part of a complex expression, and perform the manipulations on the complex expression. For example:
:
See also
*
Imaginary part
*Imaginary number
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