Answer:
The complex number has Cartesian form
.
Step-by-step explanation:
First, we need to recall the definition of when
is a complex number:
.
Then,
. (I)
Now, recall the definition of the complex exponential:
.
So,
(we use that
.
Thus,
Now we group conveniently in the above expression:
.
Now, substituting this equality in (I) we get
.
Thus,
.
The statements about the function that are true are
The equation of the graph is given as
f(x) = (x - 1)(x + 7)
The graph of the function is added as an attachment
On the graph, we have
Vertex = (-3, -16)
This is so because the graph has a minimum point of (-3, -16)
Also, the graph crosses the x-axis at x = 1 and x = -7
This means that the graph is positive at x >1 and x >-7
Because the vertex is a minimum, the graph is increasing at the left of its symmetry i.e. x > -3
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Answer:
<em>The endpoint coordinates for the mid-segment are: and
</em>
Step-by-step explanation:
According to the given diagram, the coordinates of the vertices of are:
and
Now, the endpoints of the mid-segment of which is parallel to
will be the mid-points of sides
and
.
<u>Formula for the coordinate of mid-point</u> : , where
and
are two endpoints.
So, the mid-point of will be:
and the mid-point of will be:
Thus, the endpoint coordinates for the mid-segment of that is parallel to
are
and