Explain in detail with at least two sentences how to represent the product of A and B geometrically given that A=15 + 56i and B
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Answer:
The circumference for <em>circle a</em> is m.
The circumference for <em>circle b</em> is m.
The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as or, in a less familiar form,
. The number
is constant for all circles and has infinite digits,
.
Step-by-step explanation:
The <em>circumference</em> of a circle is given by:
[1]
Where
is the circle's circumference.
is the radius of the circle.
And
is a constant value (explained below)
We can say that <em>the distance around the circle</em> is the circle's <em>circumference</em>.
The circumferences of the two circles given are:
Circle a, with radius equals to 21 meters ().
Using [1], using four decimals for , we have:
m
m
Then, the circumference for <em>circle a</em> is m.
Circle b, with radius equals to 28 meters ().
m
m
And, the circumference for <em>circle b</em> is m.
We know that
That is, the diameter of the circle is twice its radius.
Then, if we take the distance around the circle and we divided it by
This ratio, that is, the relationship between the distance around the circle (circumference) and <em>the diameter</em> of a circle is and is constant for all circles. This result is called the
number, which is, approximately,
(it has infinite number of digits).
We can observe that the relationship between the radius of a circle and the circumference is also constant:
However, this relationship is .
We can rewrite it as
And it is also constant.