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  Let \mathrm{O} be the origin and \mathrm{A} be the point \mathrm{z_{1}=1+2 i}. If \mathrm{\text { B }} is the point \mathrm{z_{2^{\prime}} \operatorname{Re}\left(z_{2}\right)<0}, such that \mathrm{OAB} is a right angled isosceles triangle with \mathrm{OB} as hypotenuse, then which of the following is NOT true?

Option: 1

\mathrm{\arg z_{2}=\pi-\tan ^{-1} 3}


Option: 2

\mathrm{\arg \left(z_{1}-2 z_{2}\right)=-\tan ^{-1} \frac{4}{3}}


Option: 3

\mathrm{\left|z_{2}\right|=\sqrt{10}}


Option: 4

\mathrm{\left|2 z_{1}-z_{2}\right|=5}


Answers (1)

best_answer

\mathrm{A B=A O \quad Z^{-i \pi / 2}=-2+i} \\

\mathrm{\text { so } O B=(-2+i)+(1+2 i)} \\

\mathrm{Z_{2}=-1-3 i} \\

\mathrm{\therefore\left|2 Z_{1}-Z_{2}\right|=\sqrt{10}}

Hence correct option is 4

 

Posted by

vishal kumar

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