TS EAMCET · Maths · Complex Number
If \(z+\frac{1}{z}=1\), then \(\frac{\left(z^{20}+1\right)\left(z^{40}+1\right)\left(z^{60}+1\right)}{z^{60}}=\)
- A -2
- B 2
- C 1
- D -1
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
If \[ z+\frac{1}{z}=1 \Rightarrow \frac{z^2+1}{z}=1 \Rightarrow z^2-z+1=0 \] So, \(\quad z=\frac{+1 \pm \sqrt{1-4}}{2} \quad z=\frac{1 \pm \sqrt{3} i}{2}\) \(\Rightarrow \quad z=-\omega\) and \(-\omega^2\) Now, for \(z=-\omega\)…
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