First slide
Algebra of complex numbers
Question

The value of Arg[iln(aiba+ib)] ; where a  and b  are real numbers

Difficult
Solution

ln(aiba+ib)=ln|aiba+ib|+i[2nπ+arg(aiba+ib)]                 =i[2nπ+arg(aiba+ib)]  |aiba+ib|=1  

Arg[iln(aiba+ib)]=Argi[2nπarg(aiba+ib)]=0orπ

As 2nπ+arg(aiba+ib)  is a real number.

 

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