Question

write the expression in the form a + bi.

\\(\sqrt{-1} + 5 - \sqrt{-49}\\)

\\(\sqrt{-1} + 5 - \sqrt{-49} = \square\\)
(simplify your answer. type your answer in the form a + bi. type an exact answer, using radicals as needed.)

Explanation:

Simplify the square root of negative one

Using the Imaginary Unit knowledge point

$$ \sqrt{-1} = i $$

Simplify the square root of negative forty-nine

Using the Imaginary Unit and Complex Numbers knowledge points

$$ \sqrt{-49} = \sqrt{49} \cdot \sqrt{-1} = 7i $$

Substitute the simplified terms back into the expression

Using the Complex Numbers knowledge point

$$ \sqrt{-1} + 5 - \sqrt{-49} = i + 5 - 7i $$

Combine the real and imaginary parts

Using the Complex Subtraction knowledge point

$$ 5 + (1 - 7)i = 5 - 6i $$

Answer:

\(\sqrt{-1} + 5 - \sqrt{-49} =\) <blank>\(5 - 6i\)</blank>