Evaluate the subtraction (13 + sqrrt -225) - (sqrrt 49 -2i)

Answer 1

To evaluate the expression \((13 + \sqrt{-225}) - (\sqrt{49} - 2i)\), let's break it down step-by-step.

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

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

3. Substitute these values into the expression: \[ (13 + 15i) - (7 - 2i) \]

4. Distribute the negative sign: \[ (13 + 15i) - 7 + 2i \]

5. Combine like terms:

   • The real parts: \(13 - 7 = 6\)
   • The imaginary parts: \(15i + 2i = 17i\)

So, combining these results gives: \[ 6 + 17i \]

The final result of the expression is: \[ \boxed{6 + 17i} \]