Question

use the properties of complex numbers to simplify (√(-49)+5i)+(8 - √(-4)). (1 point) o 8 + 5i+√(-53) o 8 + 10i o 13 + 9i o 8 + 14i

Explanation:

Step1: Simplify square - root terms

Recall that $\sqrt{-a}=i\sqrt{a}$ for $a>0$. So, $\sqrt{-49}=i\sqrt{49} = 7i$ and $\sqrt{-4}=i\sqrt{4}=2i$.

Step2: Rewrite the expression

The original expression $(\sqrt{-49}+5i)+(8 - \sqrt{-4})$ becomes $(7i + 5i)+(8-2i)$.

Step3: Combine like - terms

Combine the real parts and the imaginary parts separately. The real part is $8$, and the imaginary part is $(7 + 5-2)i=10i$. So the simplified form is $8 + 10i$.

Answer:

$8 + 10i$