Question

Select all the complex numbers in the given table

Answer 1

The complex number from the table are

`1+√(-3), \ 4-3 √(-16), \ (3+2 √(-9))/(7), \ 9 \sqrt{-(7)/(5)}`

Solution:

Let us solve and identify the complex number.

(A)
`5-\sqrt{(9)/(4)}`

`5-\sqrt{(9)/(4)}= 5-\sqrt{(3^2)/(2^2)}`

`= 5-(3)/(2)`

= 3.5

This is not a complex number.

(B)
`1+√(-3)`

`1+√(-3)=1+√(-1* 3)`

We know that
`√(-1) =i`.

`1+√(-3)=1+√(3)i`

This is a complex number.

(C)
`4-3 √(-16)`

`4-3 √(-16)=4-3 √(-1* 4^2)`

`4-3 √(-16)=4-3*4 √(-1)`

We know that
`√(-1) =i`.

`4-3 √(-16)=4-12i`

This is a complex number.

(D)
`(2-√(12))/(5)`

`(2-√(12))/(5)=(2-2√(3))/(5)`

There is no –1 in the root.

This is not a complex number.

(E)
`(3+2 √(-9))/(7)`

`(3+2 √(-9))/(7)=(3+2 √(-1* 3^2))/(7)`

We know that
`√(-1) =i`.

`=(3+6i)/(7)`

This is a complex number.

(F)
`9 \sqrt{-(7)/(5)}`

`9 \sqrt{-(7)/(5)}=9 \sqrt{-1 * (7)/(5)}`

We know that
`√(-1) =i`.

`9 \sqrt{-(7)/(5)}=9 \sqrt{ (7)/(5)}i`

This is a complex number.

Hence the complex number from the table are

`1+√(-3), \ 4-3 √(-16), \ (3+2 √(-9))/(7), \ 9 \sqrt{-(7)/(5)}`