Complex representation of harmonic time dependency facilitates multiple phase analysis based on one complex solution. Real and imaginary parts of a complex quantity
z = z0·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 = z0·cos(ωt + φz),
where z0 is a peak value of z, φz - its phase angle, and ω - the angular frequency.