Question

properties of complex numbers to simplify (rt-64+2i)+(10-rt-9)

rt means square root

Answer 1

Interpret the radicals as principal square roots of negative numbers:

sqrt(-64) = 8i and sqrt(-9) = 3i.

So
(sqrt(-64) + 2i) + (10 - sqrt(-9))
= (8i + 2i) + (10 - 3i)
= 10 + (8+2-3)i
= 10 + 7i.

(If you meant sqrt(64) or sqrt(9) instead of sqrt of negatives, tell me and I’ll recalculate.)