What is the numerator of the simplified sum? StartFraction x Over x squared + 3 x + 2 EndFraction + StartFraction 3 Over x + 1 E
ndFraction
1 answer:
Answer:
4x + 6
Step-by-step explanation:
Given
+
Before we can add the fractions we require them to have a common denominator.
Factor the denominator of the first fraction
+
Multiply the numerator / denominator of the second fraction by (x + 2)
= +
← fractions now have a common denominator
Add the numerators leaving the denominators
=
=
= ← simplified sum with numerator 4x + 6
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Answer with Step-by-step explanation:
We are given that
u+ v and u-v are orthogonal
We have to prove that u and v must have the same length.
When two vector a and b are orthogonal then
By using the property
We know that
Magnitude is always positive
When power of base on both sides are equal then base will be equal
Therefore,
Hence, the length of vectors u and v must have the same length.
Answer and step-by-step explanation:
The polar form of a complex number is the number
where
is called the modulus and
is called the argument. You can switch back and forth between the two forms by either remembering the definitions or by graphing the number on Gauss plane. The advantage of using polar form is that when you multiply, divide or raise complex numbers in polar form you just multiply modules and add arguments.
(a) let's first calculate moduli and arguments
now we can write the two numbers as
(b) As noted above, the argument of the product is the sum of the arguments of the two numbers:
(c) Similarly, when raising a complex number to any power, you raise the modulus to that power, and then multiply the argument for that value.
Now, in the last step I've used the fact that , or in other words, the complex exponential is periodic with
as a period, same as sine and cosine. You can further compute that power of two with the help of a calculator, it is around 16 million, or leave it as is.