section_path: Applications/In physics/Electromagnetism and electrical engineering
section_name: Electromagnetism and electrical engineering
paragraph_text: Electromagnetism and electrical engineering
  
  In electrical engineering, the Fourier transform is used to analyze varying voltages and currents. The treatment of resistors, capacitors, and inductors can then be unified by introducing imaginary, frequency-dependent resistances for the latter two and combining all three in a single complex number called the impedance. This approach is called phasor calculus.
  
  In electrical engineering, the imaginary unit is denoted by j, to avoid confusion with I, which is generally in use to denote electric current, or, more particularly, i, which is generally in use to denote instantaneous electric current.
  
  Because the voltage in an AC circuit is oscillating, it can be represented as
  
  V (t) = V 0 e j ω t = V 0 (cos ω t + j sin ω t), {\displaystyle V(t)=V_{0}e^{j\omega t}=V_{0}\left(\cos \omega t+j\sin \omega t\right),}
  
  To obtain the measurable quantity, the real part is taken:
  
  v (t) = Re (V) = Re = V 0 cos ω t. {\displaystyle v(t)=\operatorname {Re} (V)=\operatorname {Re} \left=V_{0}\cos \omega t.}
  
  The complex-valued signal V (t) is called the analytic representation of the real-valued, measurable signal v (t).