He will have a fourth of a cup raisins left over<span />
<h3>
Answer: 5 - 4i (choice A)</h3>
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Work Shown:
x = the other number
(5+4i)*x = 41
x = 41/(5+4i)
x = 41*(5-4i)/( (5+4i)*(5-4i) ) ..... see note below
x = 41*(5-4i)/( 41 )
x = (41/41)*(5-4i)
x = 5 - 4i
As a way to check, (5+4i)*(5-4i) = 5^2+4^2 = 25+16 = 41
The rule used is (a-bi)(a+bi) = a^2 + b^2
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Note: I multiplied top and bottom by (5-4i) to get rid of the imaginary term in the denominator.
45,000 divided by 75 is 600.
45,000/75 = 600
Since both terms are perfect squares, factor using the difference of squares formula.
a^2- b^2= (a+b) (a-b) where a=x+2y and b=2z
(x+2y+2z) (x+2y-2z)