Answer:
-5 +6i
Step-by-step explanation:
Square roots of negative numbers are imaginary. This is asking for the difference of two complex numbers. A suitable calculator can show you what that is.
__
simplify radicals
We know that √(-1) ≜ i. This means the radicals can be simplified to ...
[tex]\sqrt{-81}=\sqrt{9^2(-1)}=9\sqrt{-1}=9i\\\\\sqrt{-9}=\sqrt{3^2(-1)}=3\sqrt{-1}=3i[/tex]
So the expression becomes ...
(4 +9i) -(9 +3i)
combine terms
Like terms can be combined in the usual way. For the purpose here, i can be treated as though it were a variable.
(4 +9i) -(9 +3i) = 4 +9i -9 -3i
= (4 -9) +(9 -3)i
= -5 +6i
