How do I do this

[weary moat]

Title, solution bank is making no sense

@<791435371564892232>

@zealous plover

[royal verge]

Draw a triangle with points 0,w,w+z

[earnest charm]

could u explain your working please

[jolly thorn]

ok

lets ignore the triangle method.

[earnest charm]

i dont get why divided the sum of the arguments

[jolly thorn]

i know that the r(cos(theta)+isintheta) gives you the complex number

a+bi

when |w|=5 and argw=pi/10

we get that ugly complex number form

for the other one we are missing the |Z| value but i can find the angle

|z|(0.309016...+0.95...i)

than

arg(w+z)=pi/5

(4.755...+1.54..i+(|z|(0.309016...+0.95...i))=tan pi/5

you know how we use the technique for finding the cartesian form of the line

we gonna use the method to solve mode Z

[jolly thorn]

the first picture

i let my calculator solve it for me

than i get 2.63(1dp)

[earnest charm]

what did you make ur calc do?

ohh

u just found gradient of the line

[jolly thorn]

no, i found mode|z|

[earnest charm]

how?

[jolly thorn]

|z|0.95...+1.54../4.75...+|z|0.30...= 0.72.....

tan pi/5 is 0.72....

[earnest charm]

sorry bro idk if im being stupid but i cant wrap my head around this method

dyu mind writing out ur steps on paper please?

[jolly thorn]

sure

[earnest charm]

thanks a lot

[jolly thorn]

@earnest charm

do you understand it ?

[earnest charm]

ahh yh

i get it now

never thought about going round it like this

thanks a lot tho @jolly thorn

[jolly thorn]

this method is used to find the cartesian form of the line

[jolly thorn]

youre welcome

[earnest charm]

ah right

yhh

u just do

tan of argument

[jolly thorn]

yes

[earnest charm]

which gives gradient

[jolly thorn]

mhm

[earnest charm]

fairs

u in yr 12?

[jolly thorn]

yh

[earnest charm]

fair enough

[weary moat]

yeah the triangle i dont understand

how they got to that

[weary moat]

so you got w in mod-arg form ok, converted that to numerical form, and then after i dont understand

[weary moat]

facts drawing a picture is so overrated 🥱

[cloud rivet]

Aurora 🪻

[weary moat]

yeah from the Let |z| i dont understand

[cloud rivet]

Aurora 🪻
Compile Error! Click the reaction for more information.
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[weary moat]

shut it texit
this is the solutionbank solution which i dont understand either

[leaden stone]

@weary moat solved?

[weary moat]

no

far from it

[weary moat]

.

[weary moat]

.

[wraith gale]

@weary moat

Answer?

[weary moat]

idk 😭

[wraith gale]

Ok look

Very geometrical approach here

But make me maths mentor

Use degrees for simplicities sake

[weary moat]

#applications also i dont make people mentor its a consesus

[wraith gale]

U have to understand this

Like I said usually I’d do it in radians

But degrees for simplicities sake

If u don’t get something shout man

@weary moat

[weary moat]

the diagram at first how did you go through that

[weary moat]

nah i understand radians its alright

[wraith gale]

Nah that’s not the point

As in I don’t know the visual size of the angles

[wraith gale]

Make z

Make w

These r both vectors

Well complex numbers which we express as vectors

Then make w+z

I’m sure u know how to add vectors ur a smart person after all

But u put the ends of one to the top of the other

I did it as so

Now if u draw a line horizontal

From the point where the z component of w+z starts

U will find that the angles r corresponding

So they’re both 108

Then u find the other side of the obtuse angle in the triangle

Which can be found by doing alternate angles

Giving 18

The rest is self explanatory

[royal verge]

That’s what I would have done

But some people don’t like geo

[wraith gale]

What do they like then algebra?

It’s hella long to do that all algebraically

I think so anyways

[weary moat]

Ahhh it’s just vector addition? Then u use alternate angles, find the side using sine rule ahhh ok thank you so much! I’m gonna try write out the solution from the beginning haha thanks a lot!

Also thinking about your activity I think you’d be a good mentor tbh you explain well etc so do be sure to apply #applications if you want!!