{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# We note that as t takes on values in the interval 1 1

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s ‘modulus’, ‘argument’ and ‘principal argument’ are well-deﬁned. Concerning the modulus, if z = 0 then the point associated with z is the origin. In this case, the only r-value which can be used here is r = 0. Hence for z = 0, |z | = 0 is well-deﬁned. If z = 0, then the point associated with z is not the origin, and there are two possibilities for r: one positive and one negative. However, we stipulated r ≥ 0 in our deﬁnition so this pins down the value of |z | to one and only one number. Thus the modulus is well-deﬁned in this case, too.2 Even with the requirement r ≥ 0, there are inﬁnitely many angles θ which can be used in a polar representation of a point (r, θ). If z = 0 then the point in question is not the origin, so all of these angles θ are coterminal. Since coterminal angles are exactly 2π radians apart, we are guaranteed that only one of them lies in the interval (−π, π ], and this angle is what we call the principal argument of z , Arg(z ). I...
View Full Document

{[ snackBarMessage ]}