Simplify the following:
(6+5 i) (4-7 i)
(6+5 i) (4-7 i) = (6) (4) + (6) (-7 i) + (5 i) (4) + (5 i) (-7 i):
6×4+6 (-7 i)+5 i×4+5 i (-7 i)
6×4 = 24:
24-7×6 i+5 i×4+5 i (-7)×i
6 (-7) = -42:
24+-42 i+5 i×4+5 i (-7)×i
5×4 = 20:
24-42 i+20 i+5 i (-7)×i
5 i (-7)×i = 5 i^2 (-7):
24-42 i+20 i+-7×5 i^2
i^2 = -1:
24-42 i+20 i-7×5×-1
5 (-1) = -5:
24-42 i+20 i-7-5
-5 (-7) = 35:
24-42 i+20 i+35
24-42 i+20 i+35 = (24+35)+(-42 i+20 i) = 59-22 i:
Answer: | 59-22 i
