91Ó°ÊÓ

The locus of the complex number \(z\) in an argand plane satisfying the equation $$ \operatorname{Arg}(z+i)-\operatorname{Arg}(z-i)=\frac{\pi}{2} \text { is } $$ (A) boundary of a circle (B) interior of a circle (C) exterior of a circle (D) None of these 5

The locus of the complex number \(z\) in an argand plane satisfying the equation $$ \operatorname{Arg}(z+i)-\operatorname{Arg}(z-i)=\frac{\pi}{2} \text { is } $$ (A) boundary of a circle (B) interior of a circle (C) exterior of a circle (D) None of these

If \(z_{1}, z_{2}, z_{3}\) and \(z_{4}\) are the vertices of a square \(P Q R S\) in order, then (A) \(z_{4}+z_{2}=z_{3}+z_{1}\) (B) \(\left|z_{1}-z_{2}\right|=\left|z_{2}-z_{3}\right|=\left|z_{3}-z_{4}\right|=\left|z_{4}-z_{1}\right|\) (C) \(\left|z_{3}-z_{1}\right|=\left|z_{4}-z_{2}\right|\) (D) The real part of \(\frac{z_{1}-z_{3}}{z_{2}-z_{4}}\) is zero

If \(z_{1}, z_{2}, z_{3}\) are the vertices of an isosceles triangle and right angled at \(z_{2}\), then (A) \(z_{1}^{2}+z_{3}^{2}+2 z_{2}^{2}=2\left(z_{1}+z_{3}\right) z_{2}\) (B) \(z_{1}^{2}+z_{3}^{2}=2 z_{2}\left(z_{1}+z_{3}-z_{2}\right)\) (C) \(\left(z_{1}-z_{2}\right)^{2}+\left(z_{2}-z_{3}\right)^{2}=0\) (D) \(\frac{z_{1}-z_{2}}{z_{2}-z_{3}}\) is imaginary

If \(z\) is a complex number such that \(|z| \geq 2\), then the minimum value of \(\left|z+\frac{1}{2}\right|\) [2014] (A) is equal to \(\frac{5}{2}\) (B) lies in the interval \((1,2)\) (C) is strictly greater than \(\frac{5}{2}\) (D) is strictly greater than \(\frac{3}{2}\) but less than \(\frac{5}{2}\)