jee-main 2023 Q62

jee-main · India · session2_08apr_shift1 Complex Numbers Arithmetic Systems of Equations via Real and Imaginary Part Matching

If for $z = \alpha + i \beta , | z + 2 | = z + 4 ( 1 + i )$, then $\alpha + \beta$ and $\alpha \beta$ are the roots of the equation
(1) $x ^ { 2 } + 3 x - 4 = 0$
(2) $x ^ { 2 } + 7 x + 12 = 0$
(3) $x ^ { 2 } + x - 12 = 0$
(4) $x ^ { 2 } + 2 x - 3 = 0$

If for $z = \alpha + i \beta , | z + 2 | = z + 4 ( 1 + i )$, then $\alpha + \beta$ and $\alpha \beta$ are the roots of the equation\\
(1) $x ^ { 2 } + 3 x - 4 = 0$\\
(2) $x ^ { 2 } + 7 x + 12 = 0$\\
(3) $x ^ { 2 } + x - 12 = 0$\\
(4) $x ^ { 2 } + 2 x - 3 = 0$

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