Answer:
-15 + 8i
Step-by-step explanation:
(1 + 4i)²
(1 + 4i) (1 + 4i)
FOIL - first -- outer -- inner -- last
F -- 1 x 1 = 1
O -- 1 x 4i = 4i
I -- 4i x 1 = 4i
L -- 4i x 4i = 16i²
combine terms
1 + 4i + 4i + 16i²
simplify
1 + 8i + 16i²
(i² = -1)
simplify further
1 + 8i + (16)(-1)
1 + 8i - 16
-15 + 8i
