AP EAMCET · Maths · Complex Number
Sum of the squares of the imaginary roots of the equation \(z^8-20 z^4+64=0\) is
- A \(0\)
- B \(-12\)
- C \(-4\)
- D \(-16\)
Answer & Solution
Correct Answer
(B) \(-12\)
Step-by-step Solution
Detailed explanation
Let \(x = z^4\). \(x^2 - 20x + 64 = 0\) \((x-4)(x-16) = 0\) \(x=4\) or \(x=16\) For \(z^4=4\): \(z^2=\pm 2\). Imaginary roots come from \(z^2=-2 \Rightarrow z=\pm i\sqrt{2}\). Squares: \((-2), (-2)\). For \(z^4=16\): \(z^2=\pm 4\). Imaginary roots come from…
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