Answer:
wheres the picture?
Step-by-step explanation:
Answer:
![2+i](https://tex.z-dn.net/?f=2%2Bi)
Step-by-step explanation:
Given the expression:
![\dfrac{4+\sqrt{16-(4)(5)}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%2B%5Csqrt%7B16-%284%29%285%29%7D%7D%7B2%7D)
To find:
The expression of above complex number in standard form
.
Solution:
First of all, learn the concept of
(pronounced as <em>iota</em>) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by
.
Value of
.
Now, let us consider the given expression:
![\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i](https://tex.z-dn.net/?f=%5Cdfrac%7B4%2B%5Csqrt%7B16-%284%29%285%29%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B%5Csqrt%7B16-%284%5Ctimes%205%29%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B%5Csqrt%7B16-20%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B%5Csqrt%7B-4%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B%5Csqrt%7B%28-1%29%284%29%7D%7D%7B2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B%5Csqrt%7B%28-1%29%7D%5Csqrt4%7D%7B2%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B%5Csqrt4i%7D%7B2%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%28%5Cbecause%20%5Csqrt%7B-1%7D%20%3Di%29%20%5C%5C%5CRightarrow%20%5Cdfrac%7B4%2B2i%7D%7B2%7D%5C%5C%5CRightarrow%202%2Bi)
So, the given expression in standard form is
.
Let us compare with standard form
so we get
.
The standard form of
![\dfrac{4+\sqrt{16-(4)(5)}}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%2B%5Csqrt%7B16-%284%29%285%29%7D%7D%7B2%7D)
is: ![\bold{2+i}](https://tex.z-dn.net/?f=%5Cbold%7B2%2Bi%7D)
Answer:
Step-by-step explanation:
1 semester = 4474
8 semester = 8* 4474 35792
1 semester books = 389
8 semester books = 8* 389 <u> 3112 </u>
Total 38904
If he is going to pay this off in 10 years, he would have to have an increase of 3890.40 (after all income taxes) to pay it off. Fewer years would mean dividing by the number of years.
So for 8 years for example, he would need 4863 every year.
That number is obtained by dividing 38904 / 8
In 6 years he would need
38904/6 = 6484 extra dollars.
Answer:
5-4=1
Step-by-step explanation:
it would equal 1 since 4+1=5