Simplify the folowing expresions.
a. (4 − 2i)(5 − 3i)
b. (−2 + 3i)(−2 − 3i)
c. (1 + i)2
d. (1 + i)10 (hint: bn = (bn)mm)
e. −1 + 2i
1 − 2i
f. x2 + 4
x − 2i , provided x ≠ 2i

Acompany produces packets of soap powder labeled “giant size 32 ounces.” the actual weight of soap powder in such a box has a normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. to avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. to avoid losing money, it labels the top 5% (the heaviest 5%) overweight. how heavy does a box have to be for it to be labeled overweight?