InterviewSolution
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InterviewSolution
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If `a gt 0 and z=(1+i)^2/(a- i)` has magnitude `sqrt(2/5) then barz is ` equal toA. `1/5-3/5 i`B. `-1/5-3/5 I `C. `1/5+3/5 I `D. `-3/5-1/5 I ` |
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Answer» Correct Answer - B The given complex number `z=((1+i)^2)/(a-i)` `=((1-1+2i)(a+i))/(a^2+1)" "[ therefore i^2 = -1]` `=(2i(a+i))/(a^2+1)=(-2+2 ai )/(a^2+1)` `therefore | z|= sqrt(2//5)` `rArr sqrt(4+4a^2)/(a^2 +1)^2=sqrt(2/5)rArr (2)/(sqrt(1+a^2)=sqrt(2/5)` `rArr (4)/(1+a^2)= 2/5 rArr a^2+1 = 10 ` `rArr a^2=9 rArr a=3` `therefore z=(-2 + 6 i)/(10) " " [From Eq.(i)]` So, `barz=((-2+6i)/(10))=(-1/5+3/5i)rArr barz=-1/5-3/5i` `[ therefore if z= x+ iy , then bar z x-iy]` |
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