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

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z = x + i y z ˉ = x − i y z ˉ 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 2 + ∣ y ∣ = 0 ∣ y ∣ = ∣ y ∣ 2 y = 0 , ± 1 ⇒ i , − i are roots ​ y = 0 x 2 + ∣ x ∣ = 0 ⇒ x = 0 ⇒ α = i − i = 0 β = i ( − i ) = 1 4 ( 0 + 1 ) = 4 ​

Mathematics - Complex Number Question with Solution | TestHub

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