Not sure how to approach this
#Argand diagram
broken inlet
teal bough
Not sure how to approach this
Draw a diagram
For w and z
Notice arg(z + w) is given, and we know multiplying complex numbers adds the arguments
So find the complex numbers w and z in terms of their arguments and modulus (modulus argument form basically)
Something like this
||w = (cos(arg(w)) +sin(arg(w))i) x |w| ||
|| z = (cos(arg(z)) +sin(arg(z))i) x |z| ||
Multiply them
|| Equate to |z + w|(cos arg(z + w) + sin arg(z+w)i) ||
@broken inlet
Hope it helps
broken inlet
this is the diagram they drew but im not sure why they drew that dotted line?
and why they didnt draw 'z'
teal bough
and why they didnt draw 'z'
Didn’t bother I guess, given how crowded the diagram is already
broken inlet
This is probably the most unhelpful diagram
tell me
teal bough
I think they just wanted to focus on the new complex number product
teal bough
Draw like
Two lines starting from origin
One above one below
I guess that would help
broken inlet
i think im just confused on the purpose of the dotted line, like how to draw arg z when they didnt even draw z
broken inlet
One above one below
for w and z?
teal bough
The top one is w * z
Ok you know what
The diagrams purpose is to hint at modulus arg form
That is it
Dont sweat the diagram
broken inlet
The top one is w * z
wouldnt it be w + z?
teal bough
i think im just confused on the purpose of the dotted line, like how to draw arg...
Realised that z and w are on the same line when drawn
teal bough
wouldnt it be w + z?
Product of complex numbers
arg(w + z) is argument of the product
broken inlet
oh i see
is there a video on yt or something about this or diagram?
i get how to do normal questions except only this one
and cant find any resources that teach it
teal bough
and cant find any resources that teach it
Check TL Maths
On yt
Or use the ocr a further maths book, free download from annas archive
broken inlet
No videos before doing this
ok
teal bough
Lemme know if done
broken inlet
are you edexcel or ocr?
teal bough
Ocr