Question

write the polynomial with roots 4, -3i leading coefficient 1 degree 3

Answer 1

First, if you have one complex root then you will also have the conjugate as a root. Therefore the three factors for the polynomial would be (x-4)(x+3i)(x-3i)
Multiplying out \[\left( x+4 \right)\left( x-3i \right)\left( x+3i \right)=(x+4)(x ^{2}+9)=x ^{3}+4x ^{2}+9x+4\]

Answer 2

Use the Pythagorean theorem to calculate the length of BC. Then just siply count the other squares in the path and add to the length of BC.