Solving 8-j3)5e^-jsomething Complex Phasor Problem

[seang]

I can convert sinusoids to phasors and vice versa if they are relatively simple, but I don't know how to deal with these two.

(8-j3)5e^-jsomething.

I was going to distribute, and make two vectors and find the resultant vector, but I don't think that's how to go about it. also

Thanks ver much for any hints or secrets.

 

[phantom_photon]

I don't know how to deal with these two

Where's the second one?
Just put the first factor into polar form and multiply, like so:
(8-j3)*5*exp(-jx) = Sqrt(73)*exp(-j*0.3588)*5*exp(-jx) = 5*Sqrt(73)*exp(-j*(x+0.3588))
which converts to 42.72*Cos(wt - x - 0.3588), assuming, of course, that the phasors are of the same frequency, w.

 

[ravenprp]

Hello,

Thank you for reaching out and sharing your question. Solving complex phasor problems can be challenging, but with practice and understanding of the concepts, it can become easier.

In this case, it looks like you have a combination of a complex number (8-j3) and a phasor (5e^-jsomething). To solve this problem, you can use the following steps:

1. Convert the complex number (8-j3) into polar form. This can be done by finding the magnitude (r) and phase angle (θ) using the formula r = √(a^2 + b^2) and θ = arctan(b/a), where a is the real part and b is the imaginary part.

2. Now, we can rewrite the phasor in polar form as 5∠-jsomething, where 5 is the magnitude and -jsomething is the phase angle.

3. To find the resultant phasor, we can use the formula A∠θ = B∠ϕ, where A and B are the magnitudes and θ and ϕ are the phase angles. In this case, A = 5 and B = r, and θ = -jsomething and ϕ = θ. This will give us the resultant phasor in polar form.

4. Finally, we can convert the resultant phasor back to rectangular form using the formula x = Acos(θ) and y = Asin(θ), where x and y are the real and imaginary parts of the phasor.

I hope this helps you solve the problem. Remember to practice and familiarize yourself with the concepts of complex numbers and phasors to become more comfortable with solving these types of problems. Good luck!