ATRACTOR

1)\(z=4+3i\;\;\;\;\;\; w=2+i\)

\(\begin{array}{rcl} 4+3i & = & \left(2+i\right)\cdot2+i\\ 2+i & = & i\left(1-2i\right)+0 \end{array}\)

\(gcd\left(4+3i,2+i\right)=i\)

2) \(z=14+8i\;\;\;\;\;\; w=1+7i\)

\(\begin{array}{rcl} 14+8i & = & \left(1+7i\right)\left(1-2i\right)+\left(-1+3i\right)\\ 1+7i & = & \left(-1+3i\right)\left(2-i\right)+0 \end{array}\)

\(gcd\left(14+8i,1+7i\right)=-1+3i\)

3) \(z=25+53i\;\;\;\;\;\; w=2+14i\)

\(\begin{array}{rcl} 25+53i & = & \left(2+14i\right)\left(4-i\right)+3-i\\ 2+14i & = & \left(3-i\right)\left(-1+4i\right)+1+i\\ 3-i & = & \left(1+i\right)\left(1-2i\right)+0 \end{array} \)

\(gcd\left(25+53i,2+14i\right)=1+i\)

4)\(z=53+7i\;\;\;\;\;\; w=1+101i\)

\(\begin{array}{rcl} 53+7i & = & \left(1+101i\right)\left(-i\right)-48+8i\\ 1+101i & = & \left(-48+8i\right)\left(-2i\right)-15+5i\\ -48+8i & = & \left(-15+5i\right)\left(3\right)-3-7i\\ -15+5i & = & \left(-3-7i\right)\left(-2i\right)-1-i\\ -3-7i & = & \left(-1-i\right)\left(5+2i\right)+0 \end{array}\)

\(gcd\left(53+7i,1+101i\right)=-1-i\)