Let \( O \) be the origin and \( A \) be the point \( z_{1}=1+2 i \). If \( B \) is the point \(...

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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 \( O A B \) is a right angled isosceles triangle with \( O B \) as hypotenuse, then which of the following is NOT true?
(a) \( \operatorname{argz}_{2}=\pi-\tan ^{-1} 3 \)
(b) \( (\arg )\left(z_{1}-2 z_{2}\right)=-\tan ^{-1} \frac{4}{3} \)
(c) \( \left|z_{2}\right|=\sqrt{10} \)
(d) \( \left|2 \mathrm{z}_{1}-\mathrm{z}_{2}\right|=5 \)
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