WBJEE · Maths · Complex Number
Suppose that \(z_{1}, z_{2}, z_{3}\) are three vertices of an equilateral triangle in the angand plane. Let \(\alpha=\frac{1}{2}(\sqrt{3}+i)\) and \(\beta\) be a non-zero complex number. The points \(a z_{1}+\beta, \alpha z_{2}+\beta, \alpha z_{3}+\beta\) will be
- A the vertices of an equilateral triangle
- B the vertices of an isosceles triangle
- C collinear
- D the vertices of a scalene triangle
Answer & Solution
Correct Answer
(A) the vertices of an equilateral triangle
Step-by-step Solution
Detailed explanation
Since, \(z_{1}, z_{2}\) and \(z_{3}\) are the vertices of an equilateral triangle, therefore \[ \begin{aligned} \left|z_{1}-z_{2}\right| &=\left|z_{2}-z_{3}\right| \\ &=\left|z_{3}-z_{1}\right|=k \\ \alpha &=\frac{1}{2}(\sqrt{3}+i) \end{aligned} \] Also,…
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