If z is a complex number satisfying z 2 + 3 z 2 = - 4 , then the sum of the absolute values of the imaginary parts of the roots of the equation is

Question

If z is a complex number satisfying z 2 + 3 z 2 = - 4 , then the sum of the absolute values of the imaginary parts of the roots of the equation is, 0, 2 3, 2, 2 3 + 2

MARKS App · Accepted Answer

z 4 + 4 z 2 + 3 = 0 z 2 + 1 z 2 + 3 = 0 ⇒ z 2 = - 1 or - 3 ⇒ z = ± i , ± 3 i Hence, the required sum is 1 + - 1 + 3 + - 3

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