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 each term.

1. Evaluate \(\sqrt{-225}\): \[ \sqrt{-225} = \sqrt{225} \cdot \sqrt{-1} = 15i \] So we have: \[ 13 + \sqrt{-225} = 13 + 15i \]

2. The second part of the expression is \((49 - 2i)\). We can simply write it as is: \[ 49 - 2i \]

Now substitute these results into the expression: \[ (13 + 15i) - (49 - 2i) \]

Next, we distribute the negative sign: \[ (13 + 15i) - 49 + 2i \]

Now combine like terms:

• Real parts: \(13 - 49 = -36\)
• Imaginary parts: \(15i + 2i = 17i\)

So the entire expression simplifies to: \[ -36 + 17i \]

Therefore, the final result in the form \(a + bi\) is: \[ \boxed{-36 + 17i} \]