Answer
$-2 + 12i$
Work Step by Step
Use the definition of the square roots of negative numbers:
$4\sqrt {-9} - 2 = 4\sqrt {(-1)(9)} - 2$
Use the multiplication property of square roots to rewrite the radical:
$4\sqrt {(-1)(9)} - 2 = \sqrt {-1} \cdot \sqrt {9} - 2$
Use the definition of $i$ to substitute for $\sqrt {-1}$:
$4 \cdot i \cdot \sqrt {9} - 2$
Take the square root of $9$:
$4 \cdot i \cdot 3 - 2$
Multiply to simplify:
$12i - 2$
Rewrite the solution in a more conventional way with the imaginary number placed last:
$-2 + 12i$