Tips/Tricks for Complex Numbers (1 Viewer)

[frog1944]

Hi,

I saw the long division thread where they talked about synthetic division and I loved it! Much quicker and less room for error.

Are there any other tricks or methods that can be applied to complex numbers to reduce time it takes to solve a problem and remove potential error in the process?

Also, is there any common mistakes or struggles people have with complex numbers?

Thanks

 

[wu345]

There's a few for finding the roots of complex numbers that will save you a decent amount of time.
For one, there's completing the square eg. find the roots of 3+4i
3+4i=4+4i+i^2=(2+i)^2 , hence the roots are +-(2+i)
There's also inspection, which often works if |x|,|y| and |x+iy| form a pythagorean triad
eg. Find the roots of 7+24i
let (x+iy)^2=7+24i
upon expansion and equating real and imaginary parts, x^2-y^2=7 and xy=12.
By inspection (inspecting the factors of xy and seeing which pair fits both equations)
x=+-4,y=+-3 and since xy>0 x and y have the same sign
thus roots are +-(4+3i)
Some more nifty tricks can be found here: https://www.maths.unsw.edu.au/sites/default/files/hsc_tips_and_tricks-handbook.pdf

 

[frog1944]

Ok, thank you very much

 

[Silly Sausage]

get yourself a casio fx100au plus (BOS approved)

 

[frog1944]

How come?

 

[BLIT2014]

How come?

Can perform various calculations using complex numbers.

 

[frog1944]

Ok, thanks

 

[eyeseeyou]

Did any of you guys struggle with complex numbers

 

[BLIT2014]

Did any of you guys struggle with complex numbers

Well I'd say the topic was quite complex

 

[eyeseeyou]

Well I'd say the topic was quite complex

WHat's more complex than complex numbers (other than mechanics and harder 3U)?

 

[integral95]

WHat's more complex than complex numbers (other than mechanics and harder 3U)?

Honestly you ask way to many questions about this, it's best that you wait and see when you start doing 4U math yourself instead of speculating about it.

 

[integral95]

I'd say the common mistakes are getting the negatives the wrong way

Yeah it would depend on the types of questions.

 

[eyeseeyou]

Honestly you ask way to many questions about this, it's best that you wait and see when you start doing 4U math yourself instead of speculating about it.

Yeah but I wanna make the right choices