Solve the following recurrence relation. You will need a basic understanding of complex numbers $($what they are and how to add, subtract, multiply and divide them$)$; see the appendix in the text book or talk to the instructor.

$0=1$

c

$0$

$=$

$1$

$,1=4$

c

$1$

$=$

$4$

$,$ and $=2122$

c

n

$=$

$2$

c

n

$$

$1$

$$

$2$

c

n

$$

$2$

for $>=2$

n

$>=$

$2$

$.$