InterviewSolution
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InterviewSolution
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If `z^2+z|z|+|z^2|=0,`then the locus `z`isa. a circleb. a straight linec. a pair of straight line d.none of theseA. a circleB. a straight lineC. a pair of straing lineD. none of these |
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Answer» Correct Answer - C `z^(2)+z|z|+|z|^(2)=0` `rArr ((z)/(|z|))^(2)+(z)/(|z|)+1=0` `rArr (z)/(|z|)=omega,omega^(2)` `rArr z-omega |z|orz=omega^(2)|z|` `rArr x+iy=|z|((-1)/(2)+(isqrt3)/(2))orx+iy=|z|((-1)/(2)-(isqrt3)/(2))` `rArr =-(1)/(2)|z|,y=|z|(sqrt3)/(2)or x=-(|z|)/(2),y=(|z|sqrt3)/(2)` `rArr y+sqrt3x=0ory-sqrt(3)x=0rArr y^(2)-3x^(2)=0` |
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