For the polynomial f(z) = 3z^2 - (4+7i)z + 3 + 2i in c[x]
evaluate f(-1+2i)

12 - 11i.

Step-by-step explanation:

f(z) = 3z^2 - (4+7i)z  + 3 + 2i

f(-1 + 2i) =  3(-1 + 2i)^2 - (4 + 7i)(-1 + 2i) + 3 + 2i

= 3( 1 - 2i - 2i + 4i^2) - (-4 + 8i -7i + 14i^2) + 3 + 2i

= 3( -3 - 4i) - (-18 + i) + 3 + 2i

= -9 - 12i + 18 - i + 3 +2i

= 12 - 11i.

all about the same size in the city the game was

step-by-step explanation:

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.