InterviewSolution
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InterviewSolution
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Find all non zero complex numbers z satisfying `barz=iz^2` |
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Answer» Correct Answer - `[z =I , pm (sqrt3)/(2) - (i)/(2)]` Let z= x+iy. Given `bar z= iz^2` `rArr bar(x+ iy)=i(x+I y)^2` `rArr x-iy =i(x^2-y^2+2i xy)` `rArr x- iy = -2 xy +I ( x^2 -y^2 +2i xy)` `rArr x-iy= -2 xy +i(x^2 -y^2)` Note it is a compound equation , therefore we can generate from it more than one primary equation . On equationg real and imaginary parts equations. x= -2 xy and `x^2-y^2+y=0` `rArr x(1 +2y)=0` `rArr` x=0 or y = -1/2 When y=- 1/2 , `x^2-y^2+y=0` `rArr x^2 -1/4-1/2=0 rarr x^2 = 3/4` `rArr x=pm (sqrt3)/(2)` Therefore z=0 +i 0, 0+ i , `pm sqrt(3)/2-i/2` `rArr z=i , pm sqrt(3)/2-i/2 " " [ because z ne 0]` |
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