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Question Number 31335 by NECx last updated on 06/Mar/18
Findthepricipalvalueofz=(1−i)i
Commented by abdo imad last updated on 06/Mar/18
wehavez=eiln(1−i)andlnheremesndthecomplexelogbut1−i=2(12−i2)=e−iπ4⇒ln(1−i)=ln(2)−iπ4⇒iln(1−i)=iln(2)+π4⇒eiln(1−i)=eπ4(cos(ln(2)+isin(ln(2)))⇒(1−i)i=eπ4cos(ln(2))+ieπ4sin(ln(2)).
∣(1−i)i∣=eπ4.
Commented by NECx last updated on 06/Mar/18
thankyousomuch.
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