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

Answer 1

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

Step 1: Simplify $\sqrt{-225}$

$$\sqrt{-225}=\sqrt{225}\cdot \sqrt{-1}=15i$$ So, $13+\sqrt{-225}=13+15i$.

Step 2: Simplify $\sqrt{49}$

$$\sqrt{49}=7$$ Now substitute this back into the expression: $$(\sqrt{49}-2i)=7-2i$$

Step 3: Substitute the simplified parts back into the expression

The expression now becomes: $$(13+15i)-(7-2i)$$

Step 4: Distribute the negative sign

$$(13+15i)-7+2i=13-7+15i+2i$$

Step 5: Combine the real and imaginary parts

Real part: $$13-7=6$$ Imaginary part: $$15i+2i=17i$$

Final Result

Combining the results, we get: $$6+17i$$

Thus, the answer in the form $a+bi$ is: $$\boxed{{\displaystyle 6+17i}}$$