Two sequences and begin with values and satisfy the recursive relations above for .
Find .
How many complex numbers are there such that and
Let , , and . If the distance between and is as large as possible, then determine . Give your answer as the sum of the real and imaginary parts of .
If is a non-zero complex number, then find the minimum value of
Clarification: represent the imaginary part of .
For a complex number , find the smallest possible value of
Clarification: .