Select the correct answer. What is $$ \sqrt{-16}+\sqrt{49} $$ written as a complex number in the form $$ a+b \mathrm{i} $$ ? A. $$ -4+7 \mathrm{i} $$ B. $$ 7-4 \mathrm{i} $$ C. $$ 7+4 \mathrm{i} $$ D. $$ 4+7 \mathrm{i} $$

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UpStudy AI · Accepted Answer

We begin by rewriting the square root of a negative number:

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

Next, we evaluate the square root of a positive number:

$$
\sqrt{49} = 7.
$$

Now, we add the two results:

$$
\sqrt{-16}+\sqrt{49} = 4i + 7.
$$

Rearranging into the standard form $$ a + bi $$, we obtain:

$$
7+4i.
$$

Thus, the correct answer is:

C. $$ 7+4i $$.
The answer is $$ 7+4i $$, choice C.

Select the correct answer.
What is written as a complex number in the form ?
A.
B.
C.
D.

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