AP EAMCET · Maths · Complex Number
If \(z_1\) and \(z_2\) are two of the \(n^{\text {th }}\) roots of unity such that the line segment joining them subtends a right angle at the origin then for a positive integer \(\mathrm{k}, \mathrm{n}\) takes the form
- A 4 k
- B \(4 \mathrm{k}+1\)
- C \(4 \mathrm{k}+2\)
- D \(4 \mathrm{k}+3\)
Answer & Solution
Correct Answer
(A) 4 k
Step-by-step Solution
Detailed explanation
Let \(z_1 = e^{i\theta_1}\) and \(z_2 = e^{i\theta_2}\). As \(z_1, z_2\) are \(n^{\text{th}}\) roots of unity: \(\theta_1 = \frac{2\pi p}{n}\), \(\theta_2 = \frac{2\pi q}{n}\) for distinct integers \(p, q\). The line segment joining them subtends a right angle at the origin:…
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