for any pair of complex numbers and similarly .

Write *z*= *a*+*bi* and *w*=*c* + *di*. Using the definition of complex
conjugate
we can easily check the two statements by using the formulas given
above for multiplication and division. For example,

But we may
also notice that the conjugate of a number in standard form is
obtained by changing *i* to -*i*. Since (-*i*)(-*i*) = (*i*)(*i*) = -1,
the real part of an arbitrary algebraic expression is not affected by
changing *i* to -*i* and the
imaginary part changes sign. So
it doesn't matter if we do algebraic manipulations first and then
change *i* to -*i* or if we first change *i* to -*i* and then do the
algebra.
We will
get the same answer.

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