Question

z=4+i root 7 then z^3-4z^2-9z+91​

Answer 1

Answer:

Step-by-step explanation:

So i was learning complex numbers and i came across this problem. In the solution they have made z−4=i7–√ and then they squared the above equation resulting in z2−8z+16=−7 then they proceeded by sending −7 to the LHS resulting in z2−8z+23=0.

They then divided the original cubic term by the resulting equation from the above steps to get answer as −1. I did not understand why did they do it and how they got −1. The final equation looked like this: z3−4z2−9z+91=(z2−8z+23)(z+4)−1=−1.