91Ó°ÊÓ

Equation of tangent drawn to circle \(1 z \mid=r\) at the point \(A\left(z_{0}\right)\) is a. \(\operatorname{Re}\left(\frac{z}{z_{0}}\right)=1\) b. \(z \bar{z}_{0}+z_{0} \bar{z}=2 r^{2}\) c. \(\operatorname{Im}\left(\frac{z}{z_{0}}\right)=1\) d. \(\operatorname{Im}\left(\frac{z_{0}}{z}\right)=1\)

The complex number associated with the vertices \(A, B, C\) of \(\triangle A B C\) are \(e^{i 0}, \omega, \bar{\omega}\), respectively [where \(\omega, \bar{\omega}\) are the complex cube roots of unity and \(\cos \theta>\operatorname{Re}(\omega)]\), then the complex number of the point where angle bisector of \(A\) meets the circumcircle of the triangle, is a. \(e^{i \prime \prime}\) b. \(e^{-i \theta}\) c. \(\omega \bar{\omega}\) d. \(\omega+\bar{\omega}\)

Given \(z\) is a complex number with modulus 1 . Then the equation \([(1+i a) /(1-i a)]^{4}=z\) has a. all roots real and distinct b. two real and two imaginary c. three roots real and one imaginary d. one root real and three imaginary