Optimizing Accuracy: Complex Number Calculations for RL Circuit

[shaltera]

Homework Statement

Calculate
Z₁=5+j10
Z₂=10+j8
Z₃=10+J5
R_L=40
V=100

V_TH=VX(Z₂/Z₁+Z₂)
Z_TH=Z₃+(Z₁Z₂/Z₁+Z₂)
I=V_TH/(Z_TH+R_L)

I_L=?

Homework Equations

My question is what calculation method is more accurate:

First to convert complex numbers in polar forms, and then calculate or calculate complex number until final result and then convert in polar form?

The Attempt at a Solution

 

[NascentOxygen]

You carry along sufficient significant figures so that either gives the answer to the desired accuracy. So neither can be said to be "more accurate".

 

[SteamKing]

Ya got a little happy with the HW template.

 

[mfb]

I removed the additional copies of the homework template.

As you have to add complex numbers, I would not convert them to polar form. This increases the number of steps a lot, probably also increasing the error. I would not worry about that, however, your initial values are given with a precision of 2-3 digits, every reasonable system will calculate that with much more than 3 digits precision.

 

[gneill]

Staying in rectangular form it's possible to carry through the calculations exactly when the given values are all expressed with whole numbers. Here, for example, $I_L = \frac{12176}{13121} - j\frac{4888}{13121}$.

For practical work, though, this rarely happens, and in general all values have some uncertainty associated with them. Keep enough guard digits in all intermediate values though the calculation so that rounding and truncation doesn't introduce errors larger than your uncertainties!

Angle conversions, in particular can be troublesome since the conversions are not linear functions: plot the tan and arctan functions and see. In some parts of the curves small errors can be magnified while in other places the conversion is practically insensitive to small changes in the function argument. My advice is to keep more digits in angles than you think is necessary and never round intermediate angle values. Round only for final result presentation.