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

A box weighing 615 pounds is held in place on an inclined plane that has an angle of 14°. What force is required to hold it in place? Round to the nearest pound.

Find all nth roots of z. Write answers in polar form and plot roots in complex plane.

Convert the point to exact rectangular coordinates.

Convert the point to exact rectangular coordinates.

Find the product, z₁z₂ in rectangular form. and

Use a calculator to express the complex number in polar form. Round angle to one decimal place and in degrees.

A force with a magnitude of 470 pounds and another with a magnitude of 347 pounds are acting on an object. The two forces have an angle of 146 degrees between them. What is the magnitude of the resultant force? Round to the nearest pound.

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

Find the magnitude of the vector AB. A = (5, 24) and B = (10, 30)

Convert the equation from polar to rectangular form.

Perform the indicated vector operation. (12 i -13 j ) - (-16 i -22 j)

Convert the point to exact rectangular coordinates.

Convert the point to exact rectangular coordinates. (2, $\pi$ /2)

A ship's caption sets a course due north at 9 mph. The water is moving at 5 mph due west. What is the actual velocity of the ship, and in what direction is it traveling?

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

A force of 752 pounds is acting on an object at an angle of 77 degrees from the horizontal. Another force of 241 pounds is acting at an angle -43 degrees from the horizontal. What is the magnitude of the resultant force? Round to the nearest pound.

Find all complex solutions to the equation.

Find a unit vector in the direction angle of the vector v.

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

Express the complex number in polar form.