Question

Which of the following is a complex number?

Answer 1

The complex number is B,
`3\sqrt{(7)/(5)}+\sqrt{-(9)/(5)}`

Explanation:

A complex number should be written in the form
`a+bi`, where a and b are real numbers, and i is an imaginary number.

Recall that
`√(-1)=i`. Since letter B has the second term
`\sqrt{-(9)/(5)}`, we can say

`\sqrt{-(9)/(5)}=\sqrt{-1\cdot(9)/(5)}=i\sqrt{(9)/(5)}`

Therefore, the number can be written as

`3\sqrt{(7)/(5)}+i\sqrt{(9)/(5)}`.