InterviewSolution
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InterviewSolution
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If `z(1+a)=b+i ca n da^2+b^2+c^2=1,`then `[(1+i z)//(1-i z)=``(a+i b)/(1+c)`b. `(b-i c)/(1+a)`c. `(a+i c)/(1+b)`d. none of theseA. `(a+ib)/(1+c)`B. `(b-ic)/(1+a)`C. `(a+ic)/(1+b)`D. none of these |
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Answer» Correct Answer - A `(1+iz)/(1-izx)=(1+i(b+ic)//(1+a))/(1-i(b+ic)//(1+a))` `=(1+a-c+ib)/(1+a+c-ib)` `=((1+a-c+ib)(1+a+c+ib))/((1+a+c)^(2)+b^(2))` `=(1+2a+a^(2)-b^(2)-c^(2)+2ib+2iab)/(1+a^(2)+c^(2)+b^(2)+2ac+2(a+c))` `=(2a+2a^(2)+2ib+2iab)/(2+2ac+2(a+c))" "(therefore a^(2)+b^(2)+c^(2)=1)` `=(a^(2)+a^(2)+ib+iab)/(1+ac+(a+c))` `=(a(a+1)+ib(a+1))/((a+1)(c+1))=(a+ib)/(c+1)` |
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