Question

find an upper bound for the modulus 3z^2+2z+1 if |z|<1​

Answer 1

Answer:

The upper bound of $|3z^2+2z+1|$ is 6

Step-by-step explanation:

Using the inequality $|z_1+z_2|\le |z_1|+|z_2|$

We have,

          $|3z^2+2z+1|\le |3z^2|+|2z|+|1|$

                                 $\le 3|z|^2+2|z|+1$

                                  $<3(1)^2+2(1)+1=6,$ since $|z|<1$