JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \(O\) be the origin and \(A\) be the point \(z _{1}=1+2 i\). If \(B\) is the point \(z _{2}, \operatorname{Re}\left( z _{2}\right)<0\), such that \(OAB\) is a right angled isosceles triangle with \(OB\) as hypotenuse, then which of the following is NOT true?
- A \(\arg z _{2}=\pi-\tan ^{-1} 3\)
- B \(\arg \left(z_{1}-2 z_{2}\right)=-\tan ^{-1} \frac{4}{3}\)
- C \(\left|z_{2}\right|=\sqrt{10}\)
- D \(\left|2 z_{1}-z_{2}\right|=5\)
Answer & Solution
Correct Answer
(D) \(\left|2 z_{1}-z_{2}\right|=5\)
Step-by-step Solution
Detailed explanation
\(AB = AO \cdot z ^{-i \pi n 2}=-2+i\) So \(OB =(-2+i)+(1+2 i)\) \(z _{2}=-1+3 i\) \(\therefore\left|2 z _{1}- z _{2}\right|=\sqrt{10}\)
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