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  • Let z be a complex number such that the Imaginary part of z is non zero and a=z^2+z+1 is real , then a cannot take the value of

Let z be a complex number such that the Imaginary part of z is non zero and a=z^2+z+1 is real , then a cannot take the value of

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Solution: We have ,  

       \ Rightarrow z^2+z+(1-a)=0\\Rightarrow z=-1pm sqrt1-4(1-a)/2\ \Rightarrow z=-1pm sqrt4a-3/2

Here , a eq 3/4,otherwise z will be purely real .

Posted by

Deependra Verma

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