Mathematical Formulas for Industrial and Mechanical Engineering

but any two of them differ by some multiple of 2π. Each of these angles θ is called

an argument of z, but, by convention, one of them is called the principal argument.

Definition If z is a non-zero complex number, then the unique real number θ,

which satisfies

x 5 jzjcos θ; y 5 jzjsin θ; 2 π , θ # π

is called the principal argument of z,denotedbyθ 5 argðzÞ. Note: The distance from

the origin to the point ðx; yÞ is jzj, the modulus of z; the argument of z is the angle

θ 5 arctanðy=xÞ. Geometrically, θ is the directed angle measured from the positive

x-axis to the line segment from the origin to the point ðx; yÞ.Whenz 5 0, the angle θ

is undefined.

The ...