Question

How to determine
max|z exp(3 + iz^2)| for |z| ≤ 2

Answer 1

|z| ≤ 2 ---> max |z| = 2

max|z exp(3 + iz^2)| = max|z exp(3) exp(iz^2)| = max|z exp(3 )|max |exp(iz^2)|
now max value of e^(i theta) = 1
max|z exp(3 + iz^2)| = max|z exp(3 )|*1 = exp(3) max |z| = 2exp 3
got this ?

Answer 2

thanks