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(Solved): Define the Gaussian integers as Z[i]:={a+bi in C|a,b in Z} For z,d in Z[i], we say that d divides z ...
Define the Gaussian integers as
Z[i]:={a+bi in C|a,b in Z}
For z,d in Z[i], we say that d divides z if z=dk for some k in Z[i].
There is a Division Theorem for Z[i] in the sense that for any z_(1),z_(2 )in Z[i], there exist
q,r in Z[i] such that
z_(1)=z_(2)*q+r,|r|<|z_(2)||*| denotes the usual absolute value for complex numbersZ[i] in the same way as in Z. You may assume
that the concept of a "gcd" makes sense in Z[i] and that the last non-zero remainder in the
Z[i] Euclidean Algorithm is a gcd.
Find a greatest common divisor of 7-11i and 7-i.