Algebra
# Complex Numbers

$\large \begin{cases} {a_n=a_{n-1}a_{n-2}-b_{n-1}b_{n-2} } \\ { b_n=b_{n-1}a_{n-2}+a_{n-1}b_{n-2} } \end{cases}$

Two sequences $a_n$ and $b_n$ begin with values $a_1=b_1=a_2=b_2=1$ and satisfy the recursive relations above for $n>2$.

Find $\large \frac{b_{2015}}{a_{2015}}$.

If $Z$ is a non-zero complex number, then find the minimum value of

$\displaystyle \dfrac{\text{Im}(Z^{5})}{(\text{Im}(Z))^{5} }.$

**Clarification:** $\text{Im}(Z)$ represent the imaginary part of $Z$.

For a complex number $z$, find the smallest possible value of $|z-3|^2+|z-5+2i|^2+|z-1+i|^2.$

**Clarification:** $i=\sqrt{-1}$.