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4.29 Arithmetic of complex numbers

Arithmetic operations

(i) Addition is defined by

(a+ib)+(x+iy)=(a+x)+i(b+y)

so that complex numbers add like vectors.

(ii) Multiplication is defined by

(a+ib)(x+iy)=(ax-by)+i(ay+bx).

(iii) Conjugation is defined by refelction in the real axis, so

\overline{x+iy}=x-iy=(x+iy)^{*}