91Ó°ÊÓ

Sketch the complex number \(z\) and its complex conjugate \(z\) on the same complex plane. $$ z=8+2 i $$

Sketch a graph of the polar equation, and express the equation in rectangular coordinates. $$ r=-1 $$

Sketch the complex number \(z\) and its complex conjugate \(z\) on the same complex plane. $$ z=-5+6 i $$

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ x=\cos 2 t, \quad y=\sin 2 t $$

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ x=\sec t, \quad y=\tan t, \quad 0 \leq t<\pi / 2 $$

Sketch \(z_{1}, z_{2}, z_{1}+z_{2},\) and \(z_{1} z_{2}\) on the same complex plane. $$ z_{1}=2-i, \quad z_{2}=2+i $$

Sketch a graph of the polar equation, and express the equation in rectangular coordinates. $$ \theta=5 \pi / 6 $$

Sketch \(z_{1}, z_{2}, z_{1}+z_{2},\) and \(z_{1} z_{2}\) on the same complex plane. $$ z_{1}=-1+i, \quad z_{2}=2-3 i $$

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ x=\tan t, \quad y=\cot t, \quad 0 < t < \pi / 2 $$

\(3-24=A\) pair of parametric equations is given. (a) Sketch the curve represented by the parametric equations. (b) Find a rectangular coordinate equation for the curve by eliminating the parameter. $$ x=\tan t, \quad y=\cot t, \quad 0 < t < \pi / 2 $$