
Complex representation of harmonic time dependency facilitates multiple phase analysis based on one complex solution. Real and imaginary parts of a complex quantity
z = z_{0}·e^{ i·(ωt + φz)},
have phase angles shifted by 90 degrees, and their linear combination may be used to represent any arbitrary phase angle.
z = z_{0}·cos(ωt + φ_{z}),
where z_{0} is a peak value of z, φ_{z}  its phase angle, and ω  the angular frequency.
Related Topics
Complex Vector.