Solving quad eq with complex coefficient (2 Viewers)

[Tryingtodowell]

Doquestions like these pop up often in 4u exams? Its easy but the amount of simplifying is annoying asf and if ur not careful with the simplifying you can easily fuck up the final answer so..

 

[SMARTYPANTS_SINGH]

Doquestions like these pop up often in 4u exams? Its easy but the amount of simplifying is annoying asf and if ur not careful with the simplifying you can easily fuck up the final answer so..

i mean finding roots of any complex poly let alone a quadratric i'd say it very common. Though u can make mistakes u can always plug ur values back in to see if they work

 

[Tryingtodowell]

i mean finding roots of any complex poly let alone a quadratric i'd say it very common. Though u can make mistakes u can always plug ur values back in to see if they work

So this is common?

 

[SMARTYPANTS_SINGH]

Very, it’s like a stock standard question 11

 

[Tryingtodowell]

Very, it’s like a stock standard question 11

It takes one page to solve it (I mean I just started so I might not be efficient yet) so imagine if that was embedded in a bigger q

 

[SMARTYPANTS_SINGH]

this is just a quadratic, it gets worse

 

[Tryingtodowell]

ok yeah im prolly gonna come back in a few weeks and laugh at this. im prob just being dramatic

 

[SMARTYPANTS_SINGH]

but they are all usually easy marks just tedious, literally the same as mechanics, but mech takes more pages

 

[liamkk112]

Doquestions like these pop up often in 4u exams? Its easy but the amount of simplifying is annoying asf and if ur not careful with the simplifying you can easily fuck up the final answer so..

does your calculator not have complex numbers? on mine you can just type stuff into the calc and it'll simplify it for you, so you can just put in the quadratic formula and it'll tell you the answer
though obviously if you get something complex under the square root, you still have to find the roots of the complex number

 

[appleali]

ok so with these questions, ive seen them q11-12
usually a 2mark part i, where they ask you to find square roots of a complex number
then part ii is 2 or 3 marks and you use the quadratic equation where the square root part is the square root from part i
nothing too hard just needs some practice

 

[Sam14113]

Presumably your big time sink is finding square roots of complex numbers.

For some inexplicable reason schools very rarely teach this well.

Consider that you want to find a number x+iy such that its square is 3+4i.

By squaring both sides and equating real and imaginary components you get the equations x^2 -y^2 = 3 and 2xy = 4.

But you also get |x + iy|^2 = |3 + 4i|, from which you get x^2 + y^2 = 5.

The first and third equations are pretty trivial to solve simultaneously using elimination. The second equation will just tell you whether x and y have the same sign or different signs.

This to me is a lot easier than only using the first 2 equations. And hopefully should save you just under half a page.

 

[epicmaths]

This is amazing Sam I've actually forgotten this trick exists, although the version I've seen gets the same thing through squaring and adding eq1 and 2.

I always recommend students try get the values through inspection before they delve into time wastage >.<

 

[appleali]

This is amazing Sam I've actually forgotten this trick exists, although the version I've seen gets the same thing through squaring and adding eq1 and 2.

I always recommend students try get the values through inspection before they delve into time wastage >.<

yeah i never even thought of that method
it’s acc so good
usually i get it via inspection but when the values are non trivial then it is very useful