Answer:
3 +2i
Step-by-step explanation:
[tex]3+\sqrt{-4} =3+2\sqrt{-1}=3+2i \quad\text{assuming the positive square root}[/tex]
The number in complex number form is [tex]\bold{3 \pm 2 i}[/tex]
[tex]3+\sqrt{-4}[/tex]
Let's assume the given expression as 'A' for easy understanding.
[tex]A=3+\sqrt{-4}[/tex]
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,
[tex]\Rightarrow A=3+\sqrt{(-1) \times 4}[/tex]
[tex]\therefore A=3 \pm 2 i[/tex]
The complex numbers are always written as:
[tex]a \pm i b[/tex]
Where 'a' and 'b' are real numbers and 'i' is imaginary number.
