Let $f(z)=(z -1)(z -4)^{2}$ Find the lines (through $z=2$) on which $|f(z)|$ has a relative maximum, and the ones on which $|f(z)|$ has a relative minimum.
MY ATTEMPT:
"The line z= 2" is the line where z= 2+ ix for any real number x. Then $f(z)=(z−1)(z−4)^{2} =(2−ix−1)(2−ix−4)^{2}=(1−ix)(−2−ix)^{2}$ . Write out $|f(z)|$ as a function of x, find the derivative, set it equal to 0.