Simplify the expression

(1-3i) (2+5i) - (3-12i).

Show your work.

14 + 11i

Step-by-step explanation:

The product of binomials is found in the usual way, except that i² = - 1.

(1 - 3i) (2 + 5i) - (3 - 12i)

= (1·2 + 1·5i - 3i·2 - 3i·5i) - 3 + 12i

= (2 + 15 - 3) + i (5 - 6 + 12)

= 14 + 11i