91Ó°ÊÓ

In Exercises 1-12, write each expression as a complex number in standard form. If an expression simplifies to either a real number or a pure imaginary number, leave in that form. $$ \sqrt{-64} $$

In Exercises 1-12, graph each complex number in the complex plane. $$ -3 i $$

In Exercises 1-20, find the product \(z_{1} z_{2}\) and express it in rectangular form. $$ z_{1}=6\left(\cos 20^{\circ}+i \sin 20^{\circ}\right) \text { and } z_{2}=8\left(\cos 10^{\circ}+i \sin 10^{\circ}\right) $$

In Exercises 1-20, graph the curve defined by the following sets of parametric equations. Be sure to indicate the direction of movement along the curve. $$ x=\sqrt{t}, y=t, t \text { in }[0,10] $$

In Exercises 1-10, plot each indicated polar point in a polar coordinate system. $$ \left(-4,270^{\circ}\right) $$

In Exercises 1-20, find the product \(z_{1} z_{2}\) and express it in rectangular form. $$ z_{1}=5\left(\cos 200^{\circ}+i \sin 200^{\circ}\right) \text { and } z_{2}=2\left(\cos 40^{\circ}+i \sin 40^{\circ}\right) $$

In Exercises 1-12, write each expression as a complex number in standard form. If an expression simplifies to either a real number or a pure imaginary number, leave in that form. $$ \sqrt{-27} $$

In Exercises 1-20, graph the curve defined by the following sets of parametric equations. Be sure to indicate the direction of movement along the curve. $$ x=t, y=\sqrt{t^{2}+1}, t \text { in }[0,10] $$

In Exercises 1-12, graph each complex number in the complex plane. $$ -5 i $$

In Exercises 1-10, plot each indicated polar point in a polar coordinate system. $$ \left(3,135^{\circ}\right) $$