newton.c running with complex 
find f(x)=0 x_next = x - f(x)/f'(x) 
expect convergence, sometimes 
f(x)=x^4+1  f'(x)=4*x^3 beware x=0 
x=   1.000000000000000+   1.000000000000000i 
f(x)=  -3.000000000000000+   0.000000000000000i 
fp(x)=  -8.000000000000000+   8.000000000000000i 
i=0, x=   0.812500000000000+   0.812500000000000i 
i=1, x=   0.725897530723714+   0.725897530723714i 
i=2, x=   0.707823903513730+   0.707823903513730i 
i=3, x=   0.707107870264998+   0.707107870264998i 
i=4, x=   0.707106781189064+   0.707106781189064i 
i=5, x=   0.707106781186547+   0.707106781186547i 
i=6, x=   0.707106781186548+   0.707106781186548i 
i=7, x=   0.707106781186547+   0.707106781186547i 
i=8, x=   0.707106781186548+   0.707106781186548i 
i=9, x=   0.707106781186547+   0.707106781186547i 
i=10, x=   0.707106781186548+   0.707106781186548i 
i=11, x=   0.707106781186547+   0.707106781186547i 
sqrt(2)/2=   0.707106781186548