TS EAMCET · Maths · Complex Number
The sum of the complex roots of the equations \((x-1)^3+64=0\) is
- A 6
- B 3
- C \(6 \mathrm{i}\)
- D \(3 i\)
Answer & Solution
Correct Answer
(A) 6
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & (x-1)^3+64=0 \\ & \Rightarrow \quad(x-1)^3=-64 \\ & \Rightarrow \quad(x-1)^3=(-4)^3 \\ & \Rightarrow \quad x-1=-4,-4 w,-4 w^2 \\ & \Rightarrow \quad x=-3,-4 w+1,-4 w^2+1 \\ & \end{aligned} \] Complex roots of the equations are \[ -4 w+1,-4 w^2+1 \]…
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