use the properties of complex numbers to simplify (√-49 +5i)+(8-√-4).
- 8+14i
- 13+9i
- 8+10i
- 8+5i+√-53
First, let's simplify each term separately:
√-49 + 5i:
√-49 = √(49 * -1) = √49 * √(-1) = 7i
√-49 + 5i = 7i + 5i = 12i
8 - √-4:
√-4 = √(4 * -1) = √4 * √(-1) = 2i
8 - √-4 = 8 - 2i = 8 + (-2i) = 8 - 2i
Now, let's add the two simplified terms together:
12i + (8 - 2i) = 8 + 12i - 2i = 8 + 10i
Therefore, the simplified expression is - 8 + 10i. The correct answer is - 8 + 10i.