Question

would really love a hand with simultaneous equations please...?

Answer 1

100 = (150 +120 i)x - 150y -400y
0 = (350 -208.33 i)y + 400y -150x

Answer 2

need to work out what x and y equal
i is a constant, so doesnt need to be solved

Answer 3

What do you get if you expand all of the equations completely and collect like terms?

Answer 4

that is the collected terms, it was 15 different components, so that's pretty much the shortened version

100 = (150 +120 i)x - 550y
0 = (350 -208.33 i)y + 400y -150x

Answer 5

Well, I see multiple y terms in the second equation :-)

Answer 6

100 = 150x +120 ix - 550y
0 = 750y -208.33 iy -150x

Answer 7

i= sqrt -1

Answer 8

\[100 = (150 + 120i)x - 550y\]\[0=-150x + (750-208.33i)y\]
agreed?

Answer 9

sure

Answer 10

Okay, now you can use substitution or elimination to solve it, just as if you had something like
\[1 = 3x - 4y\]\[0=2x+3y\]

Answer 11

The algebra will definitely be a bit messier, though :-)

Answer 12

I might try solving the second equation for x in terms of y, and substituting that in the first equation, then solving for y.

Answer 13

what if i put it another way:
my answer was x=.4479 - .8574i and y =.1274 - .1361i

1. is this correct? (as my scientific calculator spat out 5 possible answers as it contains a complex number)

2. could you explain how to convert this to polar form?

Answer 14

Those answers look correct for the first 3 decimals, at least.

Answer 15

Convert the answer to polar form, or the problem?

Answer 16

the answer, or either
i'm not really clear on how to convert a vector from Rectangular form to Polar

Answer 17

To convert a complex number \(a+bi\) to polar form, you need to find the magnitude \(r\) and the angle \(\theta\).

Answer 18

\[r = \sqrt{a^2+b^2}\]
\[\theta = \tan^{-1}(\frac{b}{a})\]

Answer 19

you may need to adjust \(\theta\) to put it in the right quadrant...

Answer 20

that's awesome, cheers for that man! That is exactly what I need to do these

Answer 21

adjust... how so
wouldn't the fact that either b or a is -ve place it in the right quadrant automatically...?

Answer 22

Yeah, probably, I'm just trying to protect myself from malpractice lawsuits :-)

When in doubt, make a sketch and verify that the answer you got makes sense.

Answer 23

Actually, no, it doesn't always do it automatically. consider the case where both a and b are negative...how does arctan know the difference from identical a, b that are positive?

Answer 24

similarly, how does it distinguish between -a +b and +a -b?

Answer 25

good call, will sketch as i go
that would mirror a lot...

Answer 26

What's the context in which you're doing these? Math, physics, engineering?

Answer 27

all of the above, it's an engineering course, subject is physics, which is just sciencey maths

Answer 28

You'll be seeing a lot of these in your future, I predict :-) Electrical engineers often use \(j\) instead of \(i\)

Answer 29

this is something i vaguely remember from back when i was a school... it doesn't come into the polar equations does it...?

Answer 30

cheers for the help man, I'm going to head and practice q's

Answer 31

I don't recall seeing that before, but google is our friend :-)

the mnemonic is apparently "All Students Take Calculus" and it should be



See this page: http://mathonweb.com/help_ebook/html/cast.htm