Exam 7: Vectors, the Complex Plane, and Polar Coordinates

Express the complex number in rectangular form. 20(cos 240° + i sin 240°)

Find a unit vector in the direction of the vector v. V = <-9, 40>

Force A, at 230 pounds, and force B, at 335 pounds, make an angle of 165° with each other. Represent their respective vectors as complex numbers written in trigonometric form and solve for the resultant angle to one decimal place.

Find the result of the expression using De Moivre's theorem. Write the answer in rectangular form.

Find all nth roots of z. Write answers in polar form.

Graph the equation.

Find the quotient, in rectangular form. z₁ = 24 [ cos 78° + i sin 78° ] and z₂ = 4 [ cos 18° + i sin 18° ]

Plot the point in a polar coordinate system.

Graph the equation. r = cos 2 θ

Find all nth roots of z. Write answers in polar form.

Find the angle (round to the nearest degree) between the vectors. and

Convert the point to exact polar coordinates. Assume 0 ≤ θ ≤ 2π.

A box weighing 210 pounds is held in place on an inclined plane that has an angle of 10°. What force is required to hold it in place? Round to the nearest pound.

Convert the point to exact polar coordinates. Assume 0 ≤ θ ≤ 2π.

Find the result of the expression using De Moivre's theorem. Write the answer in rectangular form.

Determine if the vectors are orthogonal. and

A force with a magnitude of 526 pounds and another with a magnitude of 262 pounds are acting on an object. The two forces have an angle of 26 degrees between them. What is the direction of the resultant force with respect to the force 262 pounds? Round to one decimal place.

Find all complex solutions to the equation.

Determine if the vectors are orthogonal. < 30, 20 > and < -16, 24 >

Graph the equation.