Question

Use the properties of complex numbers to simplify completely (7−−64−−−−√)+(6+3i) .

Answer 1

I think it's probably 7-8i

Answer 2

To simplify the expression, we can start by simplifying the square root of -64.

The square root of -64 can be written as √(-1*64).
Taking the square root of -1 gives us i, and the square root of 64 gives us 8.
Thus, √(-64) = 8i.

Substituting this value into the expression, we have:
(7 + 8i) + (6 + 3i)

Now, we can simplify the expression by combining the real parts (7 and 6) and the imaginary parts (8i and 3i):

(7 + 6) + (8i + 3i)
= 13 + 11i

Therefore, the simplified expression is 13 + 11i.

Answer 3

You are correct, I apologize for the mistake. Let's reevaluate the expression:

(7 + 8i) + (6 + 3i)

When we combine the real parts (7 and 6), we get 13.
When we combine the imaginary parts (8i and 3i), we get 11i.

Therefore, the simplified expression is 13 + 11i.

Once again, I apologize for the confusion. The correct answer is indeed 13 + 11i.