Question

Express 3+square root -4 as a complex number

Answer 1

The number in complex number form is
`\bold{3 \pm 2 i}`

Given:

`3+√(-4)`

Solution:

Let's assume the given expression as 'A' for easy understanding.

`A=3+√(-4)`

Since, the square is always positive, we cannot get a negative number as a square. So, the square root of the negative number becomes an imaginary number because that number doesn't exist.

Now, on taking square root,

`\Rightarrow A=3+√((-1) * 4)`

`\therefore A=3 \pm 2 i`

The complex numbers are always written as:

`a \pm i b`

Where 'a' and 'b' are real numbers and 'i' is imaginary number.

Answer 2

3 +2i

Explanation:

`3+√(-4) =3+2√(-1)=3+2i \quad\text{assuming the positive square root}`