Question

question 4
part a

enter the correct answer in the box.

rewrite the expression \\(\frac{4 + \sqrt{16 - (4)(5)}}{2}\\) as a complex number in standard form, \\(a + bi\\).

Explanation:

Simplify the radical with a negative radicand

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

Substitute and simplify the numerator

$$ \frac{4 + 4i - (4)(5)}{2} = \frac{4 + 4i - 20}{2} = \frac{-16 + 4i}{2} $$

Divide by the denominator to write in standard form

$$ \frac{-16}{2} + \frac{4i}{2} = -8 + 2i $$

Answer:

Rewrite the expression \(\frac{4 + \sqrt{-16} - (4)(5)}{2}\) as a complex number in standard form, \(a + bi\).

<blank>\(-8 + 2i\)</blank>