Question

Which of these is a complex number?

Answer 1

Option: A is the correct answer.

The one which is a complex number is:

A.
`(8)/(3)+\sqrt{-(7)/(3)}`

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:

`i=√(-1)`

A)

`(8)/(3)+\sqrt{-(7)/(3)}`

This could also be written in the form of:

`(8)/(3)+\sqrt{(7)/(3)* -1}\\\\i.e.\\\\=(8)/(3)+\sqrt{(7)/(3)}\cdot √(-1)\\\\i.e.\\\\=(8)/(3)+i\cdot \sqrt{(7)/(3)}`

Hence, the number is in the form of:

a+ib

where

`a=(8)/(3)` which is a rational number and hence belong to real number

and

`b=\sqrt{(7)/(3)}` which is a irrational number and hence belong to a real number.

Answer 2

Option A is correct.

Explanation:

A complex number is that which has imaginary number i.e i in it.

We know √-1 = i

So, any term containing √-1 can be complex number.

In our question option A is only number having √-1 so, Option A i.e

`(2)/(3) + \sqrt{-(7)/(3) }` is complex number.