Question

Let z=z1/z2 where z1=tantheta +i and z2=z1. Find an expression for zn with n E N

Answer 1

$Z_0=0\\ Z_1=i+1\\ Z_2=i+1\\ Z_3=\bar{Z_2}+(-1)^2+1=3i+3\\ Z_4=\bar{Z_3}+(-1)^3=4-4i\\ So, Z_n = (-1)^{n+1}*ni+n$