Answer 1

I think for that U should minimize the value of z (impedance) ... took a certain number & then move either left or right side of that number ... if the value decreases in left then go left ...& if suddenly value starts increasing ... then go 1 step back & reduce the magnitude of increment & then again increment
//the numberof times U change magnitude of increment will determine the precision of omega ... I think with each time change in value of impedance starts becoming smaller to larger U should decrease the increment by 90%
//1 more idea , make some way of taking differentiation & then minimize the value of z & see for what value of w the value of z' is coming 0