Question

1. write \\(\sqrt{-48} - 4\\) in the form of \\(a + bi\\).

\\(-4 - 4i\sqrt{3}\\)

\\(-4 + 48i\\)

\\(-4 + 4i\sqrt{3}\\)

\\(-4 - i\sqrt{48}\\)

Explanation:

Identify the components of the expression

Using the Complex Numbers and Imaginary Numbers knowledge points
We are given the expression \(\sqrt{-48} - 4\) and need to rewrite it in standard form \(a + bi\), where \(a\) is the real part and \(bi\) is the imaginary part.

Simplify the radical term

Using the Imaginary Numbers knowledge point

$$ \sqrt{-48} = \sqrt{-1 \cdot 16 \cdot 3} = \sqrt{-1} \cdot \sqrt{16} \cdot \sqrt{3} = i \cdot 4 \cdot \sqrt{3} = 4i\sqrt{3} $$

Rearrange into standard form

Using the Complex Numbers knowledge point

$$ \sqrt{-48} - 4 = 4i\sqrt{3} - 4 = -4 + 4i\sqrt{3} $$

Answer:

• (A) \(-4 - 4i\sqrt{3}\)
• (B) \(-4 + 48i\)
• (C) \(-4 + 4i\sqrt{3}\) (Correct answer)
• (D) \(-4 - i\sqrt{48}\)