jee-main 2024 Q61

jee-main · India · session1_29jan_shift2 Complex Numbers Argand & Loci Locus Identification from Modulus/Argument Equation
Let $r$ and $\theta$ respectively be the modulus and amplitude of the complex number $z = 2 - i \left( 2 \tan \frac { 5 \pi } { 8 } \right)$, then $( r , \theta )$ is equal to
(1) $\left( 2 \sec \frac { 3 \pi } { 8 } , \frac { 3 \pi } { 8 } \right)$
(2) $\left( 2 \sec \frac { 3 \pi } { 8 } , \frac { 5 \pi } { 8 } \right)$
(3) $\left( 2 \sec \frac { 5 \pi } { 8 } , \frac { 3 \pi } { 8 } \right)$
(4) $\left( 2 \sec \frac { 11 \pi } { 8 } , \frac { 11 \pi } { 8 } \right)$
Let $r$ and $\theta$ respectively be the modulus and amplitude of the complex number $z = 2 - i \left( 2 \tan \frac { 5 \pi } { 8 } \right)$, then $( r , \theta )$ is equal to\\
(1) $\left( 2 \sec \frac { 3 \pi } { 8 } , \frac { 3 \pi } { 8 } \right)$\\
(2) $\left( 2 \sec \frac { 3 \pi } { 8 } , \frac { 5 \pi } { 8 } \right)$\\
(3) $\left( 2 \sec \frac { 5 \pi } { 8 } , \frac { 3 \pi } { 8 } \right)$\\
(4) $\left( 2 \sec \frac { 11 \pi } { 8 } , \frac { 11 \pi } { 8 } \right)$