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

How much work is done by a crane to lift a 1 ton car to a level of 10 feet?

Convert the point to exact rectangular coordinates.

Convert the equation from polar to rectangular form.

Find all complex solutions to the equation.Write answers in rectangular form.

Convert the point to exact rectangular coordinates.

Find all complex solutions to the equation.Write answers in rectangular form.

Find the product, z₁z₂ in rectangular form. z₁ = 2 [ cos 84° + i sin 84° ] and z₂ = 12 [ cos 66° + i sin 66° ]

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

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

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

Find the dot product. < -19, 24 > · < 15, 18 >

Find the dot product. < -11.6, -8.7 > · < 13, 8.6 >

Find the magnitude and direction angle of the vector u. u = (-2, -4)

Find the magnitude of the vector AB. A = (9, 18) and B = (21, 23)

Find the quotient, in rectangular form. and

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

Perform the indicated vector operation given u = < 14, 5 > and v = < 7, -3 >.

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

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

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