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Complex numbers: Solve the equation.... watch

1. Hi

Solve the equation: z^2 + 2z + 10 = 0
Find the modulus and argument of each root.

2. (Original post by SeekerOfKnowledge)
Hi

Solve the equation: z^2 + 2z + 10 = 0
Find the modulus and argument of each root.

use pythagoras to find the modulus,

so

and sohcahtoa to find the argument.

3. Use the quadratic formula to get z in Cartesian form.
Do you know how to get modulus and argument from there?
4. just solve it like you would any quadratic equation.. and you'll find that b^2 - 4ac < 0...hence giving you a complex number

Spoiler:
Show
Root-36 = iRoot36 = 6i
5. (Original post by HerrWarum)

use pythagoras to find the modulus,

so

and sohcahtoa to find the argument.

aha i see, thanks

yes Slumpy i think so:

arctan = (pi) - 3/1

modulus = sqrt 1^2 + 3^2

right?

erm Ewan im a little confussed with what you have done
6. (Original post by SeekerOfKnowledge)
aha i see, thanks

yes Slumpy i think so:

arctan = (pi) - 3/1

modulus = sqrt 1^2 + 3^2

right?
Modulus is right.
You've slightly missed what was being done on the argument, what was meant was:
argz= pi - arctan(3/1)
Although this misses the other root, which has argument:
argz=pi+ arctan(3/1(

(I've ignored the minus sign as I've considered that by taking the correct quadrant)
7. (Original post by SeekerOfKnowledge)
erm Ewan im a little confussed with what you have done
http://scholar.hw.ac.uk/site/maths/topic11.html work through that site, its useful and has diagrams explaining what you do in different quadrants..

I was just explaining at Root-36 is 6i & that its only complex because b^2 - 4ac < 0... read what Herr wrote

Just remember that the arguement is always measured from the positive x axis to the line. Its basically just a convention, since there are infinitely many ways of writing the same arguement.
8. (Original post by Ewan)
http://scholar.hw.ac.uk/site/maths/topic11.html work through that site, its useful and has diagrams explaining what you do in different quadrants..

I was just explaining at Root-36 is 6i & that its only complex because b^2 - 4ac < 0... read what Herr wrote

Just remember that the arguement is always measured from the positive x axis to the line. Its basically just a convention, since there are infinitely many ways of writing the same arguement.
oh i see. Thank you for the site.

Slumpy
oh yeah forgot to add the arctan,
but would that give me two arguments?
9. (Original post by Ewan)
http://scholar.hw.ac.uk/site/maths/topic11.html work through that site, its useful and has diagrams explaining what you do in different quadrants..

I was just explaining at Root-36 is 6i & that its only complex because b^2 - 4ac < 0... read what Herr wrote

Just remember that the arguement is always measured from the positive x axis to the line. Its basically just a convention, since there are infinitely many ways of writing the same arguement.
thanks for you help people
10. Did u quote me then delete your post?

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