Math help

2008-12-21 17:44:28

#1

Brasso: member; +1,549|7075

Quick question, how do I find one possible value of x in the equation x⁴ = -16?

I just need to know how to do this so I can solve for x via polar coordinates etc.

Last edited by haffeysucks (2008-12-21 17:44:46)

"people in ny have a general idea of how to drive. one of the pedals goes forward the other one prevents you from dying"

2008-12-21 17:45:51

#2

phishman420: Banned; +821|6126

Are you not on Christmas break? That shit can wait a couple weeks.

2008-12-21 17:46:23

#3

MAGUIRE93: High Angle Hell; +182|6639|Schofield Barracks

phishman420 wrote:
Are you not on Christmas break? That shit can wait a couple weeks.

2008-12-21 17:47:48

#4

Brasso: member; +1,549|7075

MAGUIRE93 wrote:
phishman420 wrote:
Are you not on Christmas break? That shit can wait a couple weeks.

not til wed

"people in ny have a general idea of how to drive. one of the pedals goes forward the other one prevents you from dying"

2008-12-21 17:49:31

#5

phishman420: Banned; +821|6126

haffeysucks wrote:
MAGUIRE93 wrote:
phishman420 wrote:
Are you not on Christmas break? That shit can wait a couple weeks.
not til wed

Damn, that sucks, bro. I've been done with math for > 2 yrs., so I'm of no help.

2008-12-21 17:49:31

#6

kylef: Gone; +1,352|6938|N. Ireland

haffeysucks wrote:
Quick question, how do I find one possible value of x in the equation x⁴ = -16?

I just need to know how to do this so I can solve for x via polar coordinates etc.

x4 = -16
x = 4(root)-16
x = (-)2

Just bring the x round to the otherside and do let it perform its opposite function, ie. square > square root

2008-12-21 17:51:30

#7

GodFather: Blademaster's bottom bitch; +387|6665|Phoenix, AZ

kylef wrote:
haffeysucks wrote:
Quick question, how do I find one possible value of x in the equation x⁴ = -16?

I just need to know how to do this so I can solve for x via polar coordinates etc.
x4 = -16
x = 4(root)-16
x = (-)2

Just bring the x round to the otherside and do let it perform its opposite function, ie. square > square root

this

2008-12-21 17:56:50

#8

Brasso: member; +1,549|7075

(-2)⁴ does not equal -16, it equals 16. if it were that easy i would have guessed it already. i feel like i've guessed everything.

"people in ny have a general idea of how to drive. one of the pedals goes forward the other one prevents you from dying"

2008-12-21 17:58:03

#9

Vub: The Power of Two; +188|6939|Sydney, Australia

Hang on a minute, you'll need to solve it using imaginary numbers.

Well, the solutions are:

2 cis(π/4)
2 cis(3π/4)
2 cis(-π/4)
2 cis(-3π/4)

p.s. π = pi

Last edited by Vub (2008-12-21 18:03:45)

2008-12-21 18:00:20

#10

argo4: Stand and Deliver; +86|6378|United States

ok, one solution is (2)^.5+(2)^.5i in a+bi form
you can find the other solutions by using negative or positive root 2 for the a part and negative or positive root 2 for the b part for a total of 4 solutions

you can use a graphical method for this: plot real numbers on x axis and imaginary numbers on y

edit: should be ±√2±√2i

Last edited by argo4 (2008-12-21 18:11:37)

2008-12-21 18:07:10

#11

blah: macaroni with cheeseeee; +111|6192|Croatia

x^4=-16
x^4=-16 / 4.root
x=2i

tbh it's 4th degree equation so there are for solutions

Last edited by blah (2008-12-21 18:08:22)

2008-12-21 18:11:42

#12

Vub: The Power of Two; +188|6939|Sydney, Australia

blah wrote:
x^4=-16
x^4=-16 / 4.root
x=2i

tbh it's 4th degree equation so there are for solutions

(2i)^4 = 2^4 * i^4 = 16 * 1 = 16.

2008-12-21 18:13:39

#13

Brasso: member; +1,549|7075

Vub wrote:
blah wrote:
x^4=-16
x^4=-16 / 4.root
x=2i

tbh it's 4th degree equation so there are for solutions
(2i)^4 = 2^4 * i^4 = 16 * 1 = 16.

yeah exactly. it doesn't work.

argo and vub, you guys are skipping ahead, i think i understand the rest of it and what you're explaining, but i don't know how to find a value of x in the first place.

for example, x³ = 8i. a value of x = 2i. i need to do the same thing for this problem.

Last edited by haffeysucks (2008-12-21 18:16:05)

"people in ny have a general idea of how to drive. one of the pedals goes forward the other one prevents you from dying"

2008-12-21 18:19:07

#14

bf2gammer: Member; +14|6665

wouldnt it be x=4i ?

take square root of both sides. since right side is negative, you have an i, square root of 16 is 4.

2008-12-21 18:22:44

#15

Vub: The Power of Two; +188|6939|Sydney, Australia

haffeysucks wrote:
Vub wrote:
blah wrote:
x^4=-16
x^4=-16 / 4.root
x=2i

tbh it's 4th degree equation so there are for solutions
(2i)^4 = 2^4 * i^4 = 16 * 1 = 16.
yeah exactly. it doesn't work.

argo and vub, you guys are skipping ahead, i think i understand the rest of it and what you're explaining, but i don't know how to find a value of x in the first place.

for example, x[sup]3[sup] = 8i. a value of x = 2i. i need to do the same thing for this problem.

OK:

x^4 = -16

Let x = r cisθ (r = modulus, θ = argument)
x^4 = r^4 cis4θ = -16

Therefore r^4 = 16 and cis4θ = -1.
r = 2 (as the modulus has to be positive)

cis4θ = -1
4θ = π ± 2πk for k = 0, 1, -1, -2
θ = π/4 ± πk/2
= π/4, 3π/4, -π/4 and -3π/4

Hence x = rcisθ
= 2cis(π/4) or 2cis(3π/4) or 2cis(-π/4) or 2cis(-3π/4)

Last edited by Vub (2008-12-21 18:27:11)

2008-12-21 18:23:01

#16

Brasso: member; +1,549|7075

bf2gammer wrote:
wouldnt it be x=4i ?

take square root of both sides. since right side is negative, you have an i, square root of 16 is 4.

just going purely by what the calculator says, (4i)^4 = 256

edit: processing that info Vub...

Last edited by haffeysucks (2008-12-21 18:29:43)

"people in ny have a general idea of how to drive. one of the pedals goes forward the other one prevents you from dying"

2008-12-21 18:32:52

#17

argo4: Stand and Deliver; +86|6378|United States

http://en.wikipedia.org/wiki/De_Moivre's_formula @ Applications is what Vub's doing. If you haven't learned that in class, it might be kind of hard to do it on your own though

Last edited by argo4 (2008-12-21 18:35:51)

2008-12-21 18:41:08

#18

Brasso: member; +1,549|7075

a friend just explained it to me. the critical part that i didn't get was that x⁴ = -16 is the same as -16+0i. that is the same as 16 cis 180, and from there i was able to solve it. cheers all.

"people in ny have a general idea of how to drive. one of the pedals goes forward the other one prevents you from dying"

2008-12-21 21:10:07

#19

TimmmmaaaaH: Damn, I... had something for this; +725|6884|Brisbane, Australia

I did that last semester and have already completely forgotten

https://bf3s.com/sigs/5e6a35c97adb20771c7b713312c0307c23a7a36a.png

2008-12-22 02:59:01

#20

Vub: The Power of Two; +188|6939|Sydney, Australia

TimmmmaaaaH wrote:
I did that last semester and have already completely forgotten

True there are hardly any uses in actual life which requires solving complex powers.

2008-12-22 05:29:23

#21

mcminty: Moderating your content for the Australian Govt.; +879|7166|Sydney, Australia

TimmmmaaaaH wrote:
I did that last semester and have already completely forgotten

Yeah, I did this in Semester one this year and I've forgotten too.

2008-12-22 07:57:07

#22

ReDevilJR: Member; +106|6796

The answer is 2i.

2*2*2*2 = 16, stick some imaginary numbers in there, and you've got your answer..

2008-12-22 08:16:37

#23

Yaocelotl: :D; +221|7095|Keyboard

ReDevilJR wrote:
The answer is 2i.

2*2*2*2 = 16, stick some imaginary numbers in there, and you've got your answer..

This

BF2S Forums Math help

phishman420 wrote:

MAGUIRE93 wrote:

phishman420 wrote:

haffeysucks wrote:

MAGUIRE93 wrote:

phishman420 wrote:

haffeysucks wrote:

kylef wrote:

haffeysucks wrote:

blah wrote:

Vub wrote:

blah wrote:

haffeysucks wrote:

Vub wrote:

blah wrote:

bf2gammer wrote:

TimmmmaaaaH wrote:

TimmmmaaaaH wrote:

ReDevilJR wrote:

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