Simplify the expression The root of negative nine over the quantity of three minus two i plus the quantity of one plus five i.

This will be:

[√9]/[ (3-2i) + (1+5i) ]

simplifying the above we get:

√9 / (3+1-2i+5i)

=√9 / (4+3i)

rationalizing the denominator we get:

√9 / (4-3i) * (4-3i) / (4-3i)

=[√9 (4-3i) ] / (16+9)

=[3 (4-3i) ]/25

= (12-9i) / 25

Answer: (12-9i) / 25