Which of the following best describes the set of all numbers of the forn a+bi where a and b are any real numbers and i equals square root of -1? a. rational exponents b. complex numbers c. complex fractions d. rational exponents

option: B is the correct answer.

                   B. complex numbers.

We know that a complex number is always written in the form of :

                                 a+ib

  where a and b are real numbers and i is the square root of -1.

i is called an imaginary number.

If a>0 and b>0 then the point lie in the first quadrant.

if a>0 and b<0 then the point lie in the fourth quadrant.

if a<0 and b>0 then the point lie in the second quadrant.

if a<0 and b<0 then the point lie in the third quadrant.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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