Given the complex numbers z 5 i and w 4 2i Find and simpl

Given the complex numbers z =-5 + i and w = - 4+ 2i, Find and simplity Z/w, W/Z, Z * W. Solve the inequality 9x^2 + 16 greaterthanorequalto 24_x. Skippy wishes to plant a veget able garden along one side of his house. In his garage, he found 32 linear feet of fencing. Since one side of the garden will border the house, Skippy doesn\'t need fencing along that side. What are the dimensions of the garden which will maximize the area of the garden? What is the maximum area of the garden? The cost, in cents, to produce x cups of Mountain Thunder Lemonade at Junior\'s Lemonade Stand is C(x) = 18x + 240, x greaterthanorequalto 0 and the price- demand function, in cents per cup, is p(x) = 90 - 3x, 0 lessthanorequalto x lessthanorequalto 30. Find the maximum profit.

Solution

z = -5 + i

w = -4 + 2i

A.

z/w = (-5 + i)/(-4 + 2i)

= (-5 + i)/(-4 + 2i)*[(-4 - 2i)/(-4 - 2i)]

= (-5 + i)*(-4 - 2i)*[(-4 + 2i)*(-4 - 2i)]

= (20 + 10i - 4i - 2i^2)/(16 - 4i^2)

we know that i^2 = -1

= (22 + 6i)/(20)

= 11/10 + 3i/10

B.

w/z = (-4 + 2i)/(-5 + i)

= (-4 + 2i)/(-5 + i)*[(-5 - i)/(-5 - i)]

= (-4 + 2i)*(-5 - i)*[(-5 + i)*(-5 - i)]

= (20 - 10i + 4i - 2i^2)/(25 - i^2)

we know that i^2 = -1

= (22 - 6i)/(26)

= 11/13 - 3i/13

C.

z*w = (-5 + i)*(-4 + 2i)

= (20 - 10 i - 4i + 2i^2)

= (18 - 14i)