Answer:
a/b = a * 1/b
Step-by-step explanation:
a/b = a * 1/b
this looks easy....
But what about
a / (1/b) = a*b
if you see any division, you can always multiply BOTH the numerator AND the denominator by the same amount. That is allowed because that is the same as multiiplying by the number 1.
So multiply by b/b and see what happens.
a / (1/b) = b/b * a / (1/b)
group the numerator AND the denominator
a / (1/b) = (b * a ) / b*(1/b)
a / (1/b) = (b * a ) / b/b
a / (1/b) = (b * a ) / 1
a / (1/b) = (b * a )
a / (1/b) = a*b
It is allowed because you can always multiply any number by 1 and that is because that will not change the original number. The number multiplied by 1 remains the same number.
This notion is very powerful and it can be used to turn any division into a multiplycation, and vice versa.
a / (1/b) = a*b
Answer:
This equation generalizes the patterns seen in part D, where a and b represent real numbers:
(a + bi)(a − bi) = a2 + b2.
