Evaluate the subtraction (13+−225)−(49−2i)\left(13+\sqrt{-225}\right)-\left(\sqrt{49}-2i\right)(13+

Question

−225
​
)−(
49
​
−2i). Provide the answer in the form of a+bia+bia+bi.

Answer 1

To evaluate the expression \((13+\sqrt{-225}) - (49 - 2i)\), we first simplify the components separately.

We know that \(\sqrt{-225} = \sqrt{225} \cdot \sqrt{-1} = 15i\).

Thus, we can rewrite our expression as:

\[ (13 + 15i) - (49 - 2i) \]

Now, we perform the subtraction:

1. Combine the real parts: \[ 13 - 49 = -36 \]

2. Combine the imaginary parts: \[ 15i - (-2i) = 15i + 2i = 17i \]

Putting both parts together, we have:

\[ -36 + 17i \]

Thus, the final answer in the form of \(a + bi\) is:

\[ \boxed{-36 + 17i} \]