Question

How to go from rectangular form to phasor form?

A) Perform vector addition
B) Use Euler's formula
C) Apply the Pythagorean theorem
D) Apply the law of sines

Answer 1

To convert from rectangular form to phasor form, use Euler's formula by identifying the real and imaginary parts, calculating the magnitude with the Pythagorean theorem, and finding the angle with inverse trigonometric functions, finally expressing the phasor as magnitude and angle. Option B is correct.

Step-by-step explanation:

To go from rectangular form to phasor form, you would use Euler's formula, which expresses a complex number in terms of its magnitude and angle, connecting the rectangular (a + jb) and the phasor (R∠θ) forms. Here's the process:

Identify the real part (a) and the imaginary part (b) of the rectangular form.

Calculate the magnitude of the phasor, which is the absolute value of the complex number: R = √(a² + b²), using the Pythagorean theorem.

Find the angle θ, which is the phase of the phasor: θ = atan2(b, a), using inverse trigonometric functions.

Now, you can express the phasor as R∠θ, where R is the magnitude calculated in step 2, and θ is the angle in step 3.

Note: The angle θ should be in radians for Euler's formula, and you may have to adjust the angle based on the quadrant in which the complex number lies.