For a non-zero complex number $z$, let $arg\left(z\right)$denote theprincipal argument with $\pi <arg\left(z\right)\le \pi$Then, whichof the following statement(s) is (are) FALSE?$arg\left(-1,-i\right)=\frac{\pi }{4},$where $i=\sqrt{-1}$(b) The function $f:R\to \left(-\pi ,\pi \right],$defined by $f\left(t\right)=arg\left(-1+it\right)$for all $t\in R$, iscontinuous at all points of $\mathbb{R}$, where $i=\sqrt{-1}$(c) For any two non-zero complex numbers $z_1$and $z_2$, $arg\left(\frac{z_1}{z_2}\right)-arg\left(z_1\right)+arg\left(z_2\right)$is an integer multiple of $2\pi$(d) For any three given distinct complex numbers $z_1$, $z_2$and $z_3$, the locus of the point $z$satisfying the condition $arg\left(\frac{\left(z-z_1\right)\left(z_2-z_3\right)}{\left(z-z_3\right)\left(z_2-z_1\right)}\right)=\pi$, lies on a straight line

Views: 1,122 students