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Messages - Ende Jin

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31
MAT334--Misc / Re: Quiz
« on: September 22, 2018, 01:40:41 PM »
Where did you see that? I cannot find it anywhere on website or syllabus.
And  it doesn't cover week3? only the topic until subset of the plane?

32
MAT334--Misc / What is covered in the quiz 1?
« on: September 22, 2018, 02:28:23 AM »
Since for the last two TUT, the topic of each tutorial is the same as
 the topic of the lecture in the same week instead of the previous week. I am wondering what to expect in the quiz1
Also ,for this week we covered green theorem at the end which is not mentioned in the tutorial handout at all, are we going to expect them on the quiz?

33
Thus in a test/quiz/exam, I should follow the convention of the textbook, right?

34
I am still confused. Let me rephrase the question again.
In the textbook, the definition of "arg" and "Arg" are:
$
arg(z) = \theta \Leftrightarrow \frac{z}{|z|} = cos\theta + isin\theta
$
which means $arg(z) \in \mathbb{R}$
while
$
Arg(z) = \theta  \Leftrightarrow \frac{z}{|z|} = cos\theta + isin\theta \land \theta \in [-\pi, \pi)
$
which means $Arg(z) \in [-\pi, \pi)$

While in the lecture, as you have introduced, it is the opposite and the range changes to $(-\pi, \pi]$ instead of $[-\pi, \pi)$ (unless I remember incorrectly):
Arg is defined to be
$
Arg(z) = \theta \Leftrightarrow \frac{z}{|z|} = (cos\theta + isin\theta)
$
which means $arg(z) \in \mathbb{R}$
while arg is
$
arg(z) = \theta  \Leftrightarrow \frac{z}{|z|} = cos\theta + isin\theta \land \theta \in (-\pi, \pi]
$

I am confused because if I am using the definition by the book,
when $z \in \{z : Re (z) > 0\}$
then $arg(z) \in (-\frac{\pi}{2} + 2\pi n,\frac{\pi}{2} + 2\pi n), n \in \mathbb{Z}$

35
I found that the definition of "arg" and "Arg" in the book is different from that introduced in the lecture (exactly opposite) (on page 7).
I remember in the lecture, the "arg" is the one always lies in $(-\pi, \pi]$
Which one should I use?

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