Question

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

Evaluate f(-1+2i)

Answer 1

12 - 11i.

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.