a.
b. Not exactly sure how DeMoivre's theorem is relevant, since it has to do with taking powers of complex numbers... At any rate, multiplying and
is as simple as multiplying the moduli and adding the arguments:
c. Similar to (b), except now you divide the moduli and subtract the arguments:
Answer: 230cm²
Step-by-step explanation:
>We can do this by splitting the figure into 2 trapeziums.
>Additionally, you can see that both trapeziums bear the same lengths a and b. Hence, we can use this formula: .
>Thus,
Area =
We have two points describing the diameter of a circumference, these are:
Recall that the equation for the standard form of a circle is:
Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.
For this we use the following equation:
Now, we replace and solve:
The center of the circle is (-8,-7), so:
On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation:
In this case, we will solve the delta with the center coordinate and the B coordinate.
Therefore, the equation for the standard form of a circle is:
In conclusion, the equation is the following:
