Let alpha and beta be the sum and the product | vedclass

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Question

$z=x+i y $

$\bar{z}=x-i y $

$\bar{z}^2=x^2-y^2-2 i x y $

$\Rightarrow x^2-y^2-2 i x y+\sqrt{x^2+y^2}=0 $

$\Rightarrow x=0 \quad 	ext { or

Vedclass · Accepted Answer

$4$

Vedclass · Answer

$z=x+i y $

$\bar{z}=x-i y $

$\bar{z}^2=x^2-y^2-2 i x y $

$\Rightarrow x^2-y^2-2 i x y+\sqrt{x^2+y^2}=0 $

$\Rightarrow x=0 \quad 	ext { or } $$ y=0 $

$-y^2+|y|=0 $ $ x^2+|x|=0 $

$|y|=|y|^2 $ $ \Rightarrow x=0 $

$y=0, \pm 1 $ $ \Rightarrow \alpha=i-i=0 $

$\Rightarrow i,-i $ $ \beta=i(-i)=1 $

are roots $ 4(0+1)=4$

are roots

Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar{z})^2+|z|=0, z \in C$. Then $4\left(\alpha^2+\beta^2\right)$ is equal to :

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