Answer:
41
Explanation:
Simplify the following:
(5 i + 4) (-5 i + 4)
Hint: | Multiply 4 + 5 i and 4 - 5 i together using FOIL.
(4 + 5 i) (4 - 5 i) = (4) (4) + (4) (-5 i) + (5 i) (4) + (5 i) (-5 i):
4×4 + 4 (-5 i) + 5 i×4 + 5 i (-5 i)
Hint: | Multiply 4 and 4 together.
4×4 = 16:
16 - 5×4 i + 5 i×4 + 5 i (-5)×i
Hint: | Multiply 4 and -5 together.
4 (-5) = -20:
16 + -20 i + 5 i×4 + 5 i (-5)×i
Hint: | Multiply 5 and 4 together.
5×4 = 20:
16 - 20 i + 20 i + 5 i (-5)×i
Hint: | Combine products of like terms.
5 i (-5)×i = 5 i^2 (-5):
16 - 20 i + 20 i + -5×5 i^2
Hint: | Evaluate i^2.
i^2 = -1:
16 - 20 i + 20 i - 5×5×-1
Hint: | Multiply 5 and -1 together.
5 (-1) = -5:
16 - 20 i + 20 i - 5-5
Hint: | Multiply -5 and -5 together.
-5 (-5) = 25:
16 - 20 i + 20 i + 25
Hint: | Evaluate 16 - 20 i + 20 i + 25.
16 - 20 i + 20 i + 25 = 41:
Answer: 41