Evaluate the subtraction

Question

(
13
+
√
−
225
)
−
(
√
49
−
2
i
)
. Provide the answer in the form of
a
+
b
i
.(1 point)

Answer 1

To evaluate the expression

\[ (13 + \sqrt{-225}) - (\sqrt{49} - 2i), \]

we will first simplify each part separately.

1. Simplifying \( \sqrt{-225} \): \[ \sqrt{-225} = \sqrt{225} \cdot \sqrt{-1} = 15i. \]

2. Simplifying \( \sqrt{49} \): \[ \sqrt{49} = 7. \]

Now we can rewrite the original expression with these simplifications:

\[ (13 + 15i) - (7 - 2i). \]

Next, distribute the negative sign in the second part:

\[ (13 + 15i) - 7 + 2i. \]

Now, combine the real and imaginary parts separately:

1. Real parts: \[ 13 - 7 = 6. \]

2. Imaginary parts: \[ 15i + 2i = 17i. \]

Thus, the final result is:

\[ 6 + 17i. \]

So, the answer in the form \(a + bi\) is:

\[ \boxed{6 + 17i}. \]