How do I solve for V_B

[viral swan]

divide both sides by that ()

[shell terrace]

i did

[viral swan]

so youre question isnt to solve for VB anymore

its to simplify the RHS

.close

[shell terrace]

i got 0.2433/0.203

[rough sphinx]

Solved

Post marked as solved by @viral swan.

Use .unsolved if this was a mistake.

[viral swan]

.unsolved jk but you should verify the RHS with a calculator before making sure its wrong

[rough sphinx]

Unsolved

Post marked as unsolved by @viral swan.

Use .solved to mark as solved.

[viral swan]

you shouldnt be getting a fraction

[viral swan]

you should get a number instead

[shell terrace]

well i got 1.1985

if u move the decimal

thats close to 12 💀

[viral swan]

can you show how you simplified the RHS

[shell terrace]

yeah sure

[viral swan]

j is not e^(j0)

[shell terrace]

its not

?

bruh

[viral swan]

theres a lot of things wrong here

just fix them one at a time when we come across them

[shell terrace]

ok let me

try one more time

[viral swan]

@shell terrace quick question

[shell terrace]

yeah

[viral swan]

,,e^{j\pi/2}

[final river]

mtt

[viral swan]

what do you think this simplifies to

[shell terrace]

aint that just

j

[viral swan]

lmao

gottem

[shell terrace]

wait

💀

WAIT

ok

brb

let me math

[viral swan]

no its j

but I had you stumble with that h

reminder that you cant rush this

also theres nothing stopping you from saying $$V_B=\frac{\displaystyle\frac{12e^{j0}}{62.83j}+\frac{12e^{j\pi/2}}{-79.6j}}{\displaystyle\frac{1}{62.83j}+\frac1{50}+\frac1{-79.6}j}$$ then entering the entire RHS into a calculator and getting $one$ number out

[final river]

mtt

[viral swan]

thats usually how you write it

I can confirm you get 12.000e^(-j2.073) when rounding the r and theta to three decimal places

[shell terrace]

my calculator cant do that

my calculator doesn't work with imaginary numbers

also i screwed it up

again

[viral swan]

I think its better if you write it like this so that your problem is only in calculating one big number

[shell terrace]

my calculator doesnt know what imaginary numbers are

[viral swan]

I didnt say to do that

I said to WRITE IT like that

[shell terrace]

wdym

[viral swan]

do you understand

[shell terrace]

so

write the whole thing like that

in a calculator

[viral swan]

yes

[shell terrace]

without j?

[viral swan]

no

bro

"write"

[shell terrace]

sorry

so just write it

[viral swan]

no

write it like that

[shell terrace]

on paper?

[viral swan]

no

[viral swan]

on here

[viral swan]

have this be your first line

[shell terrace]

oh okay

[viral swan]

🤦‍♂️

[shell terrace]

sorryyy

im really bad at this

[viral swan]

you gotta notice

you only understood when I gave you a direct instruction

that means 0% of this is being understood

100% of it is me telling you "write this down as your first line"

[viral swan]

what calculator are you using

[shell terrace]

fx-82ES PLUS

[viral swan]

that sounds expensive

[shell terrace]

its like $40 AUD

so approx $20 USD i think

[viral swan]

oh wait I recognize these

[shell terrace]

yeah thats mine

[viral swan]

now you can see its very good at giving you exact answers as long as youre only working with real numbers

[shell terrace]

yes

[viral swan]

so the next step is to combine like terms on the denominator
and simplify the numerator

[shell terrace]

okay

so e^{j0}

is just j

and j/j is 1

[viral swan]

no

[shell terrace]

oh

okay

no wait

[viral swan]

pay attention here

whats j times 0

[shell terrace]

0

e^0

is 1

[viral swan]

yes

dont rush

[shell terrace]

so for the first bit

12/62.83j

[viral swan]

which then simplifies to?

[shell terrace]

1200/6283

[viral swan]

wheres the j

[shell terrace]

outside

hm

but its at the bottom

[viral swan]

oh you just noticed

[shell terrace]

so its more 1/j * (1200/6283)

is 1/j = -j?

[viral swan]

correct

so its -1200/6283 j

[shell terrace]

yes

[viral swan]

now for th eother one

[shell terrace]

ok so

[viral swan]

e^(jπ/2) = j, you got that correct earlier

[shell terrace]

yea

and j/j

=1 ?

[viral swan]

yes

[shell terrace]

so then its just 12/-79.6

[viral swan]

yep

[viral swan]

then swap those so its more proper

-30/199 - 1200/6283 j

[shell terrace]

can I multiply everything by -1

to make it positive

?

[viral swan]

thats not a valid move

[shell terrace]

o okay

[viral swan]

we havent done the denominator yet

[shell terrace]

ok i swapped it

now for the denominator

i can combine the first and last fraction?

[viral swan]

yep

and the j in the denominator you know how to fix

[shell terrace]

so -j(1/62.83 + 1/79.6)

hm

no

[viral swan]

yea you gotta fix that

[shell terrace]

its 62.83 + 79.6

cause -j = 1/j

[viral swan]

and what's 1/(1/j) then

[shell terrace]

j?

[viral swan]

yea

[shell terrace]

ok i got j142.43

[viral swan]

what

[shell terrace]

wait

oops

ok i j(got 3.353 x 10^-3)

[viral swan]

you can type 0.003353 j

[shell terrace]

alr

[viral swan]

the denominator is now 0.02 + 0.003353 j

[shell terrace]

wait how did u get that

i took out 1/j

1/j = -j yes?

[viral swan]

you took out a -1/j

[shell terrace]

wait

[viral swan]

,,\frac1{-79.6j}=-\frac1j\frac1{79.6}=\frac1{79.6}j

[final river]

mtt

[shell terrace]

ah

[viral swan]

you then did -j = 1/j

so that meant you 1/(1/j) which also = j

[shell terrace]

ah

,, \frac{1}{j} \cdot \frac{1}{62.83}

[final river]

coolgamer123

[shell terrace]

for the other?

or

[viral swan]

thats correct

[shell terrace]

ah
,, -\frac{1}{j} \cdot -\frac{1}{62.83}

oh okay

s

so

,, \frac{1}{j} \cdot \frac{1}{62.83} + \frac1{-79.6j}=-\frac1j\frac1{79.6}=\frac1{79.6}j

[final river]

coolgamer123

[shell terrace]

wait shoot

[viral swan]

youll need to keep editing that

[shell terrace]

,, \frac{1}{j} \cdot \frac{1}{62.83} + \frac1{79.6}j

[final river]

coolgamer123

[viral swan]

1/j is?

[shell terrace]

-j

,, \frac{-j}{j} \cdot \frac{1}{62.83} + \frac{j}{79.6}j

,, \frac{-j}{62.83} + \frac{j}{79.6}j

[viral swan]

no idea what youre doing

[shell terrace]

,, \frac{-j}{62.83} + \frac{j}{79.6}

[final river]

coolgamer123

[shell terrace]

there?

[viral swan]

yea

then?

[shell terrace]

cross multiply

?

[viral swan]

no need

just subtract the fractions with your calculator

[shell terrace]

what do i put in place of j

[viral swan]

🤔

[viral swan]

,,\qty(\frac1{79.6}-\frac1{62.83})j

[final river]

mtt

[viral swan]

subtract the fractions with your calculator

youre combining like terms

[shell terrace]

okay

,, -3.353 \cdot 10^{-3}

[final river]

coolgamer123

[shell terrace]

with the j

-0.003353 j

or that

[viral swan]

wait I think we accidentally swapped something

[shell terrace]

oh

wait shouldnt it be

,,\qty(-\frac1{79.6}-\frac1{62.83})j

[final river]

coolgamer123

[shell terrace]

wait no

[viral swan]

nvm we had it correct

what are you doing

[shell terrace]

yea

-0.003353 j

[viral swan]

sure

[shell terrace]

,, V_B=\frac{-\frac{30}{199}-\frac{1200}{6283}j}{0.003353 j+0.02}

[final river]

coolgamer123

[viral swan]

swap the 0.02 and the 0.003353j as before

now we have the second line done

[shell terrace]

convert to polar form?

[viral swan]

this is done so that in the third line, you have the convert to polar form formulas only use one number

also try this

write as a separate step what numbers you put in

so √((-30/199)^2 + (-1200/6283)^2) would be part of the third step

[shell terrace]

okay

[viral swan]

what number you get out of will be part of the fourth step

[shell terrace]

oops i meant r_2 for the second part

and obv phi_1. and phi_2

[viral swan]

your arctan formula only works for numbers with positive real parts

figure out how to get that fixed

[shell terrace]

wait i need to find

principal argument?

wait no

[viral swan]

you dont need to write it out like that, you could just
[V_B=\frac{\displaystyle\sqrt{\qty(-\frac{30}{199})^2+\qty(-\frac{1200}{6283})^2}e^{\qty(\pi+\arctan\frac{1200/6283}{30/199})i}}{\sqrt{0.02^2+(-0.003353)^2}e^{\arctan\qty(\frac{-0.003353}{0.02})i}}]

[shell terrace]

or that yeah

[final river]

mtt

[viral swan]

this is now your third step

the arctan(y/x) formula only works if x > 0

for x < 0 you do arctan(y/x) + π

also you get to add/subtract 2π to the angle at any time in case its not in the range you want

[shell terrace]

i did it like this:

,, \pi - (-0.1661)

,, \pi - (-0.1661)

[final river]

coolgamer123

[shell terrace]

,, \pi + 0.1661

[final river]

coolgamer123

[shell terrace]

C:

[viral swan]

???

[shell terrace]

wait wrong one

wait shouldnt it

,, \pi - 0.9026006

[final river]

coolgamer123

[shell terrace]

because like its in the tan quadrant of the unit circle

[viral swan]

you just keep throwing things at the wall with no regard to how they fit in

go fix up the latex before you continue

[viral swan]

not going to consider what gymnastics you did to think this is correct

[shell terrace]

.close