Complex numbers - help needed

markjay

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Anyone.....?

Math.jpg


I am struggling to help my daughter with material I studied half a century ago.... :(
 

GLK

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Tried to type in here, but can't make the superscript, so a screenshot:

30532061406_0fbe75c090_o.png


... I think ... it's been 35 years at least :dk:


PS Sorry, should've included the formula: (a+bi)(c+di) = (ac−bd) + (ad+bc)i
 
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markjay

markjay

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Tried to type in here, but can't make the superscript, so a screenshot:

... I think ... it's been 35 years at least :dk:

PS Sorry, should've included the formula: (a+bi)(c+di) = (ac−bd) + (ad+bc)i

Thanks GLK! This looks correct (to my untrained eye). Will check with her tomorrow....
 

MercedesDriver

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GLK said:
Tried to type in here, but can't make the superscript, so a screenshot: ... I think ... it's been 35 years at least :dk: PS Sorry, should've included the formula: (a+bi)(c+di) = (ac−bd) + (ad+bc)i
And now this brings to mind Moivres theorem and I can't sleep.
 

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Tried to type in here, but can't make the superscript, so a screenshot:

30532061406_0fbe75c090_o.png


... I think ... it's been 35 years at least :dk:


PS Sorry, should've included the formula: (a+bi)(c+di) = (ac−bd) + (ad+bc)i

I'm usually struggling with my Tesco bill. What application would this stuff have in the real world? Serious question.
 

GLK

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What application would this stuff have in the real world?

No idea ...

I didn't even remember at first what complex numbers were, or what imaginary number is, for that matter (was it always called that?).

It took a few minutes to recall, and I was told that, at my age, I should always welcome a chance to exercise little grey cells :wallbash:
 

Palfrem

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The only imaginary number I can bring to mind is the number of glasses of vin rouge I tell my wife I enjoyed before bed.
 

GLK

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The only imaginary number I can bring to mind is the number of glasses of vin rouge I tell my wife I enjoyed before bed.

So, basically you go to bed with a bunch of square roots of minus one :thumb:


PS My wife and I enjoy our wine together, so I don't get a chance to employ higher maths there :dk:
 

Tim203

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Apparently you need to know the rules for imaginary number: i x i = -1 square root of -1 = i 15 is correct as GLK said. My work colleague and GLK are clever, that's all I can add to it. Right over my head!
 

lisa110rry

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I'm pretty hot with Excel/Access calculations but they are always centred around cost recovery on construction projects. I could not begin to understand the aforementioned!
 

knighterrant

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Druk said:
I'm usually struggling with my Tesco bill. What application would this stuff have in the real world? Serious question.
First off, electrical engineers like me use "j" because "i" is almost always used to mean "current" in our equations. Where most people would write "a + bi", we'd write "a + bj", but it means the same thing.
Electrical engineers often have to solve "differential equations" (remember them), which are a bit hard to explain without delving into calculus. Basically, a differential equation relates functions to their rates of growth. The solution to a differential equation is usually a function, not a number. As a specific example (keeping away from electrical engineering), suppose you have a snowplow that keeps piling up more and more snow in front of it so that the further it goes, the heavier the load it is pushing, and the heavier the load, the slower it goes, and the slower it goes the slower the pile of snow in front of it grows. You can (with a differential equation) relate the amount of snow at a given time t [call it A(t)] to the velocity of the plow, and the equations can be solved to give the function A(t) at all times t. But often, it's easier to solve differential equations in the domain of complex numbers because the equations are a lot nicer, but you know that the solution you care about is just the real part of the solution.
Sorry, that was making sense as I wrote it, but now that I read it with an imaginary new hat on, it'a not great as an answer. So I'll just have to say that there are uses for complex numbers in some fields, just not those filled with potatoes for Tesco.
 

Steveml63

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First off, electrical engineers like me use "j" because "i" is almost always used to mean "current" in our equations. Where most people would write "a + bi", we'd write "a + bj", but it means the same thing.
Electrical engineers often have to solve "differential equations" (remember them), which are a bit hard to explain without delving into calculus. Basically, a differential equation relates functions to their rates of growth. The solution to a differential equation is usually a function, not a number. As a specific example (keeping away from electrical engineering), suppose you have a snowplow that keeps piling up more and more snow in front of it so that the further it goes, the heavier the load it is pushing, and the heavier the load, the slower it goes, and the slower it goes the slower the pile of snow in front of it grows. You can (with a differential equation) relate the amount of snow at a given time t [call it A(t)] to the velocity of the plow, and the equations can be solved to give the function A(t) at all times t. But often, it's easier to solve differential equations in the domain of complex numbers because the equations are a lot nicer, but you know that the solution you care about is just the real part of the solution.
Sorry, that was making sense as I wrote it, but now that I read it with an imaginary new hat on, it'a not great as an answer. So I'll just have to say that there are uses for complex numbers in some fields, just not those filled with potatoes for Tesco.

Hi,
For me, one of the more complex real world maths applications must be in formula 1.
The teams need to work out whether to send cars out on hard or soft tyres for different amounts of laps vs lap times vs pit stop times - plus factor in the reducing weight of the car as it burns fuel.
It must have been even more complex when you could refuel and therefore have higher and lower weights during the race!
Cheers
Steve
 

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