Answer:
Option: A is the correct answer.
The one which is a complex number is:
A. [tex]\dfrac{8}{3}+\sqrt{-\dfrac{7}{3}}[/tex]
Step-by-step explanation:
We know that the complex number is one which is expressed in the form of :
a+ib
where a and b belongs to the set of real numbers.
and i is known as a imaginary number which is represented by:
[tex]i=\sqrt{-1}[/tex]
A)
[tex]\dfrac{8}{3}+\sqrt{-\dfrac{7}{3}}[/tex]
This could also be written in the form of:
[tex]\dfrac{8}{3}+\sqrt{\dfrac{7}{3}\times -1}\\\\i.e.\\\\=\dfrac{8}{3}+\sqrt{\dfrac{7}{3}}\cdot \sqrt{-1}\\\\i.e.\\\\=\dfrac{8}{3}+i\cdot \sqrt{\dfrac{7}{3}}[/tex]
Hence, the number is in the form of:
a+ib
where
[tex]a=\dfrac{8}{3}[/tex] which is a rational number and hence belong to real number
and
[tex]b=\sqrt{\dfrac{7}{3}}[/tex] which is a irrational number and hence belong to a real number.
