JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let a complex number be \(w =1-\sqrt{3} i\). Let another complex number \(z\) be such that \(|z w|=1\) and \(\arg ( z )-\arg ( w )=\frac{\pi}{2} .\) Then the area of the triangle with vertices origin, \(z\) and \(w\) is equal to ........ .
- A \(4\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(w =1-\sqrt{3} . i \Rightarrow| w |=2\) Now, \(| z |=\frac{1}{| w |} \Rightarrow| z |=\frac{1}{2}\) and \(\operatorname{amp}( z )=\frac{\pi}{2}+\operatorname{amp}( w )\) \(\Rightarrow\) Area of triangle \(=\frac{1}{2} \cdot OP.OQ\)…
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