Hi I need help for the following question,

1.) Let Z1 = 2cis(pi/6) and z2 = rcis(delta) where r>0, and 0<=delta<2pi.

FInd the range of values of r and delta for which z1z2 is

a.) a real number greater than 5

For the modulus of z1z2, I got r>5/2, which was right.

However for the delta, I'm not sure how I'm supposed to do it, it is (pi/6) + delta >5 and then solve the inequality? Seems wrong..

b.) a purely imaginary number with modulus less than 1

How do I find the imaginary number?

Thank you so much for your time, I really appreciate it!

J.