Calculate (1+i)^200=?

Because the exponent 200 could be written as 2*100, we'll
calculate first (1+i)^2.

We'll expand the binomial using
the formula:

(a+b)^2 = a^2 + 2ab +
b^2

a = 1 and b = i

(1+i)^2 =
1^2 + 2*1*i + i^2, where i^2 = -1

(1+i)^2 = 1 + 2i -
1

We'll eliminate like
terms:

(1+i)^2 = 2i

Now, we'll
write (1+i)^200 = [(1+i)^2]^100

 [(1+i)^2]^100 =
(2i)^100

(2i)^100 =
2^100*i^100

We'll recall the power of
i:

i^2 = -1

i^3 = i^2*i = -1*i
= -i

i^4 = i^2*i^2 = (-1)*(-1) =
1

We'll write 100 as a multiple of
4:

100 = 4*25

i^100 =
(i^4)^25

i^4 = 1

i^100 =1^25 =
1

(1+i)^200 = 2^100 = (2^4)^25 =
16^25

Identify the first revelation into Othello's character at the beginning of this section in Shakespeare's Othello:"This fellow’s of exceeding...

Othello's soliloquy beginning with "This fellow's of exceeding
honesty," occurs in Act 3, scene 3. This scene is commonly referred to as the "Temptation Scene,"
for it is in this scene that we see Iago persuading Othello that Desdemona has been unfaithful to
him. In this speech, we see many of the reasons why Othello is vulnerable to Iago's persuasion.
The first reason is perhaps in the first line of the speech. Othello expresses complete trust in
Iago's honesty and experience. As a military man, Othello is more inclined to believe the men
under his command than the new wife he has just married.

Also, in
this speech, we see the first signs of insecurity in Othello. He begins to list all the reasons
why Desdemona might possibly turn from him:

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haply, for I am black

And
have not those soft parts of conversation

That chamberers have, or
for I am declined

Into the vale of years--yet that's not
much--

Here we see that Othello
believes that his race, age, and lack of eloquence are reasons that Desdemona would fall out of
love with him. And of course, these characteristics find their opposites in Cassio, who is white,
young, and eloquent.

Not only is Othello insecure about himself, but
he, as most of the men in the play, is quick to underestimate women. He groups them into one
category, believing that these "delicate creatures" have sexual appetites that cannot be
controlled, and that women are destined to make their husbands cuckolds. He believes that being a
cuckold is a "destiny unshunnable," fated to great men when they are in the
womb.

Thus, in this speech, we see Othello's faith and trust in
Iago; his insecurities about his race, age, and background; his chauvinistic ideas about
women.

Some argue that less politically homogeneous districts might result in divisive elections. Do you believe this might be a problem? Why or Why not?

I do not believe that this would be a problem.  We might
get more divisive elections, but our Congress would be less divided and more able to
work together.

Our politically homogeneous districts lead
to very extreme candidates getting elected (even if the elections are pretty calm).  If
your district is all Republican, the most extreme Republican is likely to win.  If the
district has lots of Democrats and Independents, a moderate will be more likely to
win.

If you have moderates winning (even if the elections
are contentious) they will be more able to cooperate with other moderates from both
parties.  This would lead to a better Congress that could actually govern from the
center instead of fighting between polar opposites.

So the
elections might be tougher and nastier, but the people elected would be more likely to
work together well and we'd all be better off.

Please refer
to the link for a similar argument, made in more detail.

In act 5, what methods does Shakespeare use to create suspense? What are specific examples from the play?GOD BLESS!!

Shakespeare's Act 5 is full of suspense.  The most
effective way of achieving suspense is the short scenes that alternate between Macbeth
in the castle and the gathering of forces outside the castle.  We see Macbeth's fear,
determination, and ultimately courage as he becomes more aware of what we already know:
thousands of men are ready to do battle against him.  As the scenes alternate in a fast
paced way between Macbeth's growing realization of the ominous developments and the
joint forces of Malcolm and Siward and Macduff, the readers are anticipating a final
showdown, and the final fight scene does not
disappoint.

Related to the shift in scenes is Macbeth's
repetition of the prophecies that we begin to see developing in somewhat unexpected
ways.  When we first learn that the combined forces are meeting in Birnam Woods, we are
wondering how the witches' prophecies will be fulfilled.  Then, we learn that Birnam
Woods will come to Dunsinane as each soldier uses a bough so that the strength of their
force cannot be discovered.   We already know that Macbeth should beware Macduff who is
seeking vengeance for his slain wife and children.  And we are waiting to see how the
last prophecy will be fulfilled:  "No one born of woman shall harm Macbeth."  Macbeth
repeats this last prophecy several times--when he kills young Siward, for instance.  It
is not until Macbeth and Macduff face each other, that we learn that Macduff was not
born of woman.  This surprising information leads us to anticipate the ensuing fight
between the two.

In "A Good Man is Hard to Find," why does the author believe violence is needed in her stories to get the attention of her readers?

This is a great question. Flannery O'Connor was a very devout
Christian and thus it is perhaps strange that her fiction contains such violence. Yet, from her
perspective the violence that she writes about is specifically to highlight the fact that our
spirits live in a temporal world. The violence indicates the way that the civilisation and
culture we live in is "civilised" only in its veneer - delve to deep and you come across the
violence that we are all subject to.

In this great tale we see that
O'Connor presents us with two characters who in their separate ways are shown to be capable of
redemption. The grandmother, in spite of her selfishness, experiences a moment of grace when she
recognises that the Misfit is human just like her, when she calls him one of her "own children."
The Misfit likewise shows that he recognises that there is no pleasure in life at all. Killing no
longer gives him happiness, which suggests that he too is capable of
change.

How do the chapters in The Red Badge of Courage show that Wilson is a dynamic character rather than a static one? Cite details for support.

Wilson, the Loud Soldier, is one of the most dynamic
characters in The Red Badge of Courage. He is in a state of
constant change throughout much of the novel. He begins as the Loud Soldier--boastful,
cocky and thoroughly sure of himself--in the early chapters until he gets his first
taste of action. Just prior to the first Confederate attack, Wilson approaches Henry and
tells him that he has just had a premonition that it's "my first and last battle, old
boy." He hands Henry a packet of personal belongings, and directs him to deliver them to
his family after his death. No more is heard of Wilson until after Henry returns to the
regiment. Wilson is now strangely silent. He and Henry, who is perceived to have been
wounded in fighting behind the lines, seem to have switched characters: Henry is now the
cocksure one, while Wilson becomes quiet and unsure of himself. When the next attack
comes, Wilson holds his ground while Henry pursues the enemy as they retreat. The
regiment, including Wilson, marvels at Henry's new courage and
heroicism.

When the regiment counterattacks, Henry picks up
the fallen regimental colors and leads them at the forefront; Wilson follows his friend
at the head of the charge. Henry and Wilson are hailed as heroes. On the final attack,
Wilson captures the enemy battle flag. He, like Henry, has survived the day and is
confident in his behavior as a soldier.

In The Hobbit, on what special day do Bilbo and the dwarves discover a way into the Lonely Mountain and how do you know?

We are given the answer to this question at the end of
Chapter 3, when Elrond helps them work out where they need to go and tells them about
moon runes. Reference is made to "Durin's Day," which pleases the dwarves incredibly
because Durin is actually an ancestor of Thorin and a very important person for dwarves
in general. Note what is said about Durin's day:

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"The first day of the dwarves' New Year," said
Thorin, "is as all should know the first day of the last moon of Autumn on the threshold
of Winter. We still call it Durin's Day when the last moon of Autumn and the sun are
in the sky together."

So,
reference is made to the importance of Durin's day, however it is not clear in the novel
if they actually discover the way in to the mountain on Durin's Day itself - no mention
in Chapter 4 is made of any particular day except for the fact that winter is coming and
it is getting much colder.