Question

Express 3+square root -4 as a complex number

Answer 1

Answer:

  3 +2i

Step-by-step explanation:

$3+\sqrt{-4} =3+2\sqrt{-1}=3+2i \quad\text{assuming the positive square root}$

Answer 2

Answer:

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

Given:

$3+\sqrt{-4}$

Solution:

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

$A=3+\sqrt{-4}$

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,

$\Rightarrow A=3+\sqrt{(-1) \times 4}$

$\therefore A=3 \pm 2 i$

The complex numbers are always written as:

$a \pm i b$

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