Find the magnitude and direction angle

Question

Find the magnitude and direction angle of p = 42i + 35j

Answer 1

42i + 35j is a complex number with a real part of 42 and an imaginary component of 35

 

The magnitude is found using the Pythagorean theorem: c² = a² + b² where a is the real component and b is the imaginary component .

 

The magnitude is the square root of  = 42² + 35² or 54.67

 

The direction angle is the inverse tangent of the imaginary component divided by the real component.

 

tan^-1(35÷42) = tan^-1(.83333) = 39.8 degrees

 

Magnitude of 54.67 with a direction of 39.8 degrees