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Let z be a complex number such that |z| + z = 3 + i (Where `i=sqrt(-1))` Then ,|z| is equal toA. `sqrt(34)/3`B. `5/3`C. `sqrt(41)/4`D. `5/4` |
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Answer» Correct Answer - B We have `|z|+z=+i` Let z=x+iy `therefore sqrt(x^2+y^2)+x+iy+3+i` `rArr (x+sqrt(x^2+y^2))+iy=3+i` `rArr x+sqrt(x^2+y^2)=3 and y=1` Now , `sqrt(x^2+1)=3-x` `rArr x^2+1=9-6x+x^2` `rArr 6x=8 rArr x=4/3` `therefore z=4/3+i` `rArr |z|=sqrt(16/9)+1=sqrt(25/9) rArr |z|=5/3` |
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