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In order to work with these complex numbers without drawing vectors, we first need some kind of standard mathematical notation. There are two basic forms of complex number notation:
*
polar
*
and
*
rectangular
*
.

Polar form is where a complex number is denoted by the
*
length
*
(otherwise known as the
*
magnitude
*
,
*
absolute value
*
, or
*
modulus
*
) and the
*
angle
*
of its vector (usually denoted by an angle symbol that looks like this: ∠). To use the map analogy, polar notation for the vector from New York City to San Diego would be something like “2400 miles, southwest.” Here are two examples of vectors and their polar notations: (Figure
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)

*
Vectors with polar notations.
*

Standard orientation for vector angles in AC circuit calculations defines 0
^{
o
}
as being to the right (horizontal), making 90
^{
o
}
straight up, 180
^{
o
}
to the left, and 270
^{
o
}
straight down. Please note that vectors angled “down” can have angles represented in polar form as positive numbers in excess of 180, or negative numbers less than 180. For example, a vector angled ∠ 270
^{
o
}
(straight down) can also be said to have an angle of -90
^{
o
}
. (Figure
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) The above vector on the right (7.81 ∠ 230.19
^{
o
}
) can also be denoted as 7.81 ∠ -129.81
^{
o
}
.

*
The vector compass
*

Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides. Rather than describing a vector’s length and direction by denoting magnitude and angle, it is described in terms of “how far left/right” and “how far up/down.”

These two dimensional figures (horizontal and vertical) are symbolized by two numerical figures. In order to distinguish the horizontal and vertical dimensions from each other, the vertical is prefixed with a lower-case “i” (in pure mathematics) or “j” (in electronics). These lower-case letters do not represent a physical variable (such as instantaneous current, also symbolized by a lower-case letter “i”), but rather are mathematical
*
operators
*
used to distinguish the vector’s vertical component from its horizontal component. As a complete complex number, the horizontal and vertical quantities are written as a sum: (Figure
below
)

CloudFlare now has a consumer DNS service that is very fast and also centered around privacy. CloudFlare DNS says they won’t log IP addresses or sell your data, which in the modern era is perhaps more important than ever for users who value the vague concept of internet privacy.

This article will show you how to setup and use CloudFlare DNS on a Mac.

For some quick background, DNS is what links an IP address to an easy to read domain name, and it’s sort of like an internet directory service. The faster the DNS requests are, the faster your general internet performance will be because there is less time spent performing lookups to associate an IP address to a domain name. No, it won’t increase the actual transfer speeds, but using faster DNS may increase the response time of accessing various internet services and websites. But as mentioned above, it’s not just speed that makes Cloudflare DNS enticing, it’s the privacy-centric nature of the service, if you’re interested in learning more you can read more here from Cloudflare .

If you’re already familiar with
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then this process should be familiar to you, the main difference then is the addition of the Cloudflare DNS IP of 1.1.1.1 and 1.0.0.1. Here are the full steps:

When you apply the network setting changes your internet connection will likely temporarily disconnect and reconnect again.

You should not need to quit and relaunch any networking apps for the change to take effect, but to be thorough you may want to anyway. Or you can reboot your computer.

Likewise it shouldn’t be necessary to flush DNS caches but you’re welcome to clear DNS cache anyway, you can learn how to
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,
Sierra
, El Capitan, and other Mac OS X versions if need be.

If you have multiple Macs and decide you want to use CloudFlare DNS on all of them, you’ll want to repeat the same
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setup process on each of them, and you could also
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if you want to set those to use the service as well.

This is a great question, since every user and every ISP will likely have different performance for different DNS providers. Fortunately there are multiple ways to check DNS performance:

If you want to run a DNS comparison speed test yourself from your own Mac, and you’re savvy with the command line, you can save
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(via
cleanbrowsing
) to your local directory, and then run the following command:

Keep reading to see why it is important to dose properly (and therefore follow our two golden rules).

It'll save you from a lot of headache in the future.

Phenibut is a powder that can be ingested in various ways. Here are the three most popular methods:

If you are working with phenibut powder directly, then this is the fastest method.

This is a slightly more popular method that takes some extra steps to help you avoid the bitter taste of phenibut.

As should be obvious, by replacing water with something sweeter like fruit juice, you can minimize the taste.

This is the
**
most popular method hands-down,
**
as it is quite convenient compared to dealing with phenibut in its powder form directly.

Luckily for you, we have an extensive article on phenibut capsules.

Check it out!

Ultimately, the choice is up to you, as long as the proper dosage of phenibut makes it into your digestive tract.

First off, it is important to note that it will take about
**
30 minutes
**
before you start to feel the effects of phenibut.

This will give you an idea of when to take phenibut (i.e. 30 minutes before you want to start feeling it).

As a general guideline, before the effects start to wear off significantly, a typical dosage of phenibut will last:

However, the effects can easily last the rest of the day, to varying degrees.

This is because phenibut's action on the GABA receptors can linger long after it's been excreted from your kidney.

And obviously, taking over or under the typical dosage will vary the length accordingly.

Having said that, in general, you may start seeing
**
diminishing returns after 5-6 hours.
**

You can always take another dose, but again, we strongly advise against taking more than 2000g of phenibut in a 24-hour period.

Here are three important reasons to dose properly.

Phenibut withdrawal is when you stop taking phenibut too quickly.

When withdrawal happens, you typically experience undesired physical symptoms like nausea, tremors, and restlessness.

Withdrawal can happen with other drugs as well.

For example, the caffeine in coffee: If you're used to taking 3 cups a day, and then suddenly stop drinking, then you may experience a caffeine withdrawal.

Phenibut Tolerance is when you require larger and larger doses of a drug to get the same level of effects as the first time you took the drug.

Foreword by Yong Zhao

**
From the authors of the best-selling
Habits of Mind
…
**

A costly gap exists between what we claim to value as educational essentials and how we evaluate results. In
**
Dispositions
**
, Arthur L. Costa and Bena Kallick present a game-changing look at why and how to “mind the gap”.

The authors’
*
Habits of Mind
*
writings have influenced educational policy worldwide.
*
Dispositions
*
incorporates new cognitive science that shows how influencing students’ mental habits is their key to finding meaning in classroom content. Topics include:

Featuring techniques for integrating dispositional learning into the Common Core,
*
Dispositions
*
is Costa and Kallick’s most indispensable work on 21st Century learning.

*
“Education must include the development of the human elements in our children. Costa and Kallick present a reasonable, practical and positive alternative—the cultivation of dispositional thinking, the very core of being human.”
*
Foreword by Yong Zhao

*
“Education must include the development of the human elements in our children. Costa and Kallick present a reasonable, practical and positive alternative-- the cultivation of dispositional thinking, the very core of being human. “
*

Should you need additional information or have questions regarding the HEOA information provided for this title, including what is new to this edition, please email sageheoa@sagepub.com . Please include your name, contact information, and the name of the title for which you would like more information. For information on the HEOA, please go to http://ed.gov/policy/highered/leg/hea08/index.html .

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