JEE Main20244 Apr 2024Morning ShiftMathematicsComplex NumberActual

Let and be the sum and the product of all the non-zero solutions of the equation ( z )^2+|z|=0 , z C. Then 4 ( ^2+ ^2 ) is equal to :

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Correct answer

D. 4

Step-by-step solution

array ll z=x+i y & z =x-i y & z ^2=x^2-y^2-2 i x y & x^2-y^2-2 i x y+ x^2+y^2 =0 x=0 or & y=0 -y^2+|y|=0 & x^2+|x|=0 |y|=|y|^2 & x=0 y=0, 1 & =i-i=0 i,-i & =i(-i)=1 are roots & 4(0+1)=4 array

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