In what ways did the tragic deaths of Brutus and Caesar result from their nature or character?How would I begin an essay introduction with the answer?

Very good question. I will sketch a few ideas for you to
develop and then consider your question about the introduction to help you frame your
response.

To answer this question you need to go back and
consider the characteristics of these characters and how they are exhibited in the play.
In particular, you need to focus on their shortcomings or characteristics which are
exploited by other characters and result in their
downfall.

For example, Caesar´s major fault that results in
his assassination is his own arrogance or sense that he cannot be harmed. As Calphurnia
says to him in Act II scene 2, when she is desperately trying to persuade her husband
not to leave that day:

readability="5">

Alas, my lord,

Your
wisdom is consumed in
confidence.

It is this sense
of his own strength and invincibility that leads him to ignore the warnings of his wife,
the Soothsayer and others:

readability="10">

Caesar shall forth. The things that threatened
me

Neér looked by on my back. When they shall
see

The face of Caesar, they are
vanished.

Such a strong
self-belief in his own strength and power is arguably what leads to Caesar ignoring the
premonitions of other characters and his
assassination.

With Brutus we need to consider how his
honour, his defining characteristic, is manipulated and played upon by Cassius in the
famous seduction scene in Act I scene 2, and then leads him to make some misguided
decisions. Chief among these is his underestimation of the character of Marc Antony. It
is Brutus who persuades the conspirators not to kill him and then allows Marc Antony to
address the crowd. He dismisses the character of Marc Antony as one how is "given/to
sports, to wildness, and to much company." He also wants to strike a moderate balance
between the murder that he sees as necessary and an all-out
slaughter:

readability="18">

Our course will sem to bloody, Caius
Cassius,

To cut the head off and then hack the
limbs,

Like wrath in death and envy
afterwards;

For Antony is but a limb of
Caesar.

Let´s be sacrificers, but not butchers,
Caius.

In fact, Brutus´ own
sense of honour and what we can identify as his naivety leads him to ignore the advice
of the far more politically aware and shrewd Cassius.

In
your introduction then you need to introduce your two key ideas about these characters
and briefly explain how you are going to elaborate on their characteristics. Remember,
in the introduction you are to sketch an outline of how you are going to answer the
question. The biggest failing of most students is that they begin to answer the question
in their introduction - this should only be done in the main essay. Good
luck!