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Mathematics · 术语表

什么是 Argument, trigonometric and exponential forms?

又称: argument

Definition 28.8 High School Mathematics · 第 28 章 — Complex Numbers

Let z≠0z \neq 0. An argument of zz, written arg⁡(z)\Arg(z), is any measure θ\theta of the angle from the positive real axis to the ray OMOM; it is defined up to 2kπ2k\pi. Writing r=∣z∣r = \abs z,

z=r(cos⁡θ+isin⁡θ)(trigonometric form).z = r(\cos\theta + \iu\sin\theta) \qquad\text{(trigonometric form)}.

Introducing the notation

eiθ=cos⁡θ+isin⁡θ,\eu^{\iu\theta} = \cos\theta + \iu\sin\theta,

this becomes the exponential form z=r eiθz = r\,\eu^{\iu\theta}.

Exponential form: z is determined by its distance r to the origin and the angle  from the positive real axis.
Exponential form: zz is determined by its distance rr to the origin and the angle θ\theta from the positive real axis.
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