Simplify the expression (−7−−100−−−−√)−(−15−−81−−−−√) .(1 point) Responses −8+i negative 8 plus i 8−i 8 minus i 8−19i 8 minus 19 i −22+19i
To simplify the given expression:
(-7 - (-100 - (-√(-81)))) - (-15 - (-√(-81)))
First, let's simplify the innermost parentheses:
(-7 - (-100 - (√(-81)))) - (-15 - (√(-81)))
Next, let's simplify the square root of -81:
(-7 - (-100 - (√81i))) - (-15 - (√81i))
Since the square root of 81 is 9 and √i = i, we can simplify this further:
(-7 - (-100 - (9i))) - (-15 - (9i))
Next, let's simplify the -7 - (-100 - 9i):
(-7 + 100 + 9i) - (-15 - 9i)
Simplifying further:
(93 + 9i) - (-15 - 9i)
Next, let's simplify -15 - 9i:
(93 + 9i) + (-(15 + 9i))
Simplifying further:
93 + 9i - 15 - 9i
Combining like terms:
(93 - 15) + (9i - 9i)
Simplifying further:
78 + 0i
Finally, we can write the simplified expression as:
78 + 0i
So the answer is 78.