TS EAMCET · Maths · Complex Number
If \(z, \bar{z},-z,-\bar{z}\) forms a rectangle of area \(2 \sqrt{3}\) square units, then one such \(z\) is
- A \(\frac{1}{2}+\sqrt{3} i\)
- B \(\frac{\sqrt{5}+\sqrt{3} i}{4}\)
- C \(\frac{3}{2}+\frac{\sqrt{3} i}{2}\)
- D \(\frac{\sqrt{3}+\sqrt{11} i}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}+\sqrt{3} i\)
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) Then, vertices of rectangle are \((x, y),(x,-y)\), \((-x,-y),(-x, y)\). Now, area of rectangle \(=(2 x)(2 y)=4 x y\) It is given that,…
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