Question

The force on an object is represented by the complex number 8+21i, where the components are measured in pounds.

4) Find the magnitude of the force.
5) Find the direction of the force.

Unsure as to how to go about this problem.

Answer 1

The complex number 8 + 21i is representing a vector of coordinates 8 and 21.

a) Magnitud of the force

Then, the magnitud of the force is the module of the complex number = √[8^2 + 21^2] = √[64 + 441] = √505 = 22.47 pounds

b) Direction of the force.

The direction is given by the angle fo the vector with the positive horizontal axis, which you find using trigonometric ratios"

tan(angle) = 21/8 = 2.625 => angle = arctan(2.625) = 69.45 degrees.