Find the magnitude and direction of the resultant of the sum of 2 + 3i and 4 + 7i which are in complex notation.
A)8.00 with direction of 31.0°
B)11.66 with direction of 59.0°
C)5.66 with direction of 59.0°
D)11.66 with direction of 31.0°

Question

Quizplus · Accepted Answer

To find the resultant, we add the real parts and imaginary parts separately:

Real part: 2 + 4 = 6 
Imaginary part: 3i + 7i = 10i

So the complex number representing the resultant is 6 + 10i.

To find the magnitude of the resultant, we use the Pythagorean theorem:

|6 + 10i| = sqrt((6^2) + (10^2)) = sqrt(136) ≈ 11.66

To find the direction (in degrees) of the resultant, we use the inverse tangent function:

tanθ = (10/6) = 1.666... 
θ = atan(1.666...) ≈ 59.0°

Therefore, the magnitude of the resultant is 11.66 and the direction is 59.0°, so the best choice is B.

Find the Magnitude and Direction of the Resultant of the Sum