Multiplying and subtracting coordinates

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SUMMARY

The discussion centers on the mathematical operations involving complex numbers in polar form, specifically the calculation of |Δ| using the formula |Δ| = |S11 S22 - S12 S21|. The values provided are S11 = 0.894 ∠ -60.6, S21 = 3.122 ∠ 123.6, S12 = 0.020 ∠ 62.4, and S22 = 0.781 ∠ -27.6. The correct approach involves multiplying the magnitudes and adding the angles for the products, followed by subtraction of the two results to find |Δ| = |0.696 ∠ -83|. The participant initially struggled but successfully solved the problem after taking a break.

PREREQUISITES
  • Understanding of complex numbers in polar form
  • Knowledge of multiplication and subtraction of complex numbers
  • Familiarity with converting between polar and Cartesian coordinates
  • Basic trigonometry for angle manipulation
NEXT STEPS
  • Study the multiplication of complex numbers in polar form
  • Learn about the geometric interpretation of complex number operations
  • Explore the conversion techniques between polar and Cartesian coordinates
  • Investigate applications of complex numbers in electrical engineering
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Students studying electrical engineering, mathematicians dealing with complex numbers, and anyone interested in mastering polar coordinate operations.

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Hello,

I am hoping someone can help me understand a problem in a textbook. It just assumes you know how to do a littel bit of maths, which I don't, and haven't been able to figure out.

S11 = 0.894 [itex]\angle[/itex] -60.6
S21 = 3.122 [itex]\angle[/itex] 123.6
S12 = 0.020 [itex]\angle[/itex] 62.4
S22 = 0.781 [itex]\angle[/itex] -27.6

Then, how does |Δ| = |S11 S22 - S12 S21| = |0.696 [itex]\angle[/itex] -83|

I have tried different things, for example, converting between cartesian and polar etc, but nothing seems to get me there.

Multiplying the respective r parts, and subtracting as needed seemed to get me close there, but doing the same with the angles didn't work out.

Thanks.

-S
 
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Oh, sorry ...I just figured it out!

Taking a break and coming back to it does help.

...just a thought, should I explain how it is done in case anyone else is looking to know this sort of thing?

I don't know what the protocol would be on that.

Slán
-S
 

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