Use the properties of complex numbers to simplify completely (7−−64−−−−√)+(6+3i) .
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.
I think it's probably 7-8i
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.
To simplify the given expression, (7−√64)+(6+3i), we can start by simplifying the square root of 64.
The square root of 64 is 8, since 8 multiplied by itself gives 64.
So, we can rewrite the expression as:
(7−8)+(6+3i)
Simplifying further, we get:
-1 + (6+3i)
Next, we can simplify the addition of -1 and (6+3i) by adding their real and imaginary parts separately.
The real part of -1 and (6+3i) is -1+6 = 5.
The imaginary part of -1 and (6+3i) is 0+3 = 3.
Therefore, the simplified expression is:
5 + 3i