Question

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:

Step1: Calculate discriminant

$\sqrt{16 - (4)(5)} = \sqrt{16 - 20} = \sqrt{-4}$

Step2: Simplify imaginary root

$\sqrt{-4} = \sqrt{4 \times (-1)} = 2i$

Step3: Substitute back and split fraction

$\frac{4 + 2i}{2} = \frac{4}{2} + \frac{2i}{2}$

Step4: Simplify each term

$2 + 1i$

Answer:

$2 + i$