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Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Monopoly on November 16, 2010, 01:30:58 pm

Title: Complex number help
Post by: Monopoly on November 16, 2010, 01:30:58 pm: help me to solve this question:

the roots of the equation
z²+ 2z+4=0
are denoted by a and b. Find a and b in the form re^itheta, giving the exact values of r and theta.

for the theta of re^itheta, does the range -pie<theta=<pie still applies?
Title: Re: Complex number help
Post by: elemis on November 16, 2010, 01:48:29 pm: The easiest method to solve this is to simply solve the quadtratic equation as it is is given.

Thus the roots are $-1-i\sqrt{3}$ and $-1+i\sqrt{3}$

I guess you want those in modulus-argument form ?

Therefore it should be :

2(cos 2pi/3 + i sin 2pi/3)

2(cos -2pi/3 + i sin -2pi/3)
Title: Re: Complex number help
Post by: Monopoly on November 16, 2010, 03:30:09 pm: Quote from: Ari Ben Canaan on November 16, 2010, 01:48:29 pm
The easiest method to solve this is to simply solve the quadtratic equation as it is is given.
Thus the roots are $-1-i\sqrt{3}$ and $-1+i\sqrt{3}$
I guess you want those in modulus-argument form ?
Therefore it should be :
2(cos 2pi/3 + i sin 2pi/3)
2(cos -2pi/3 + i sin -2pi/3)

the asked modulus form is bugging me, ???
the ans given is 2e^i(2pie/3) & 2e^i(4pie/3)
Title: Re: Complex number help
Post by: astarmathsandphysics on November 17, 2010, 08:46:32 am: One hour
Title: Re: Complex number help
Post by: astarmathsandphysics on November 17, 2010, 10:30:35 am: To change into polar form
2(cos 2pi/3 + i sin 2pi/3) =2cos 2pi/3 +2isin 2pi/3
R=sqrt((2cos 2pi/3)^2+(2sin 2pi/3)^2) =2 ang arg =2pi/3 etc
Title: Re: Complex number help
Post by: Monopoly on November 17, 2010, 11:10:18 am: Quote from: astarmathsandphysics on November 17, 2010, 10:30:35 am
R=sqrt((2cos 2pi/3)^2+(2sin 2pi/3)^2) =2 ang arg =2pi/3 etc

didn't get this part...

another question
-------> a + bi is called the cartesian form
-------> r(cos theta + i sin theta) is called the modulus-argument form
-------> |u|e^itheta is the polar form?
Title: Re: Complex number help
Post by: Monopoly on November 17, 2010, 11:19:01 am: oh when they ask to sketch locus like |z-a|=k, i have difficulty to draw a god circle. So, it is necessary that the circle should be completely round?
Do i need to use a compass and make accurate drawings like the circle and in drawing perpendicular bisectors in case of l z-a l=l z-b l ?

Also, which locus are included for the CIE A2 maths syllabus. It will be really helpful if they are listed.

thanks
Title: Re: Complex number help
Post by: Monopoly on November 20, 2010, 06:26:12 am: someone?
Title: Re: Complex number help
Post by: Monopoly on November 22, 2010, 05:51:38 pm: :(
Title: Re: Complex number help
Post by: astarmathsandphysics on November 23, 2010, 08:40:15 pm: When they say sketch they mean circle like, not an artist' drawing. A VERY ROUGH SKETCH
Title: Re: Complex number help
Post by: TJ-56 on December 10, 2010, 08:55:28 pm: Write the polynomial 9z² - 6z + 5 as a product of linear factors
pls explain
thanx in advance
Title: Re: Complex number help
Post by: elemis on December 22, 2010, 11:48:33 am: Quote from: TJ-56 on December 10, 2010, 08:55:28 pm
Write the polynomial 9z² - 6z + 5 as a product of linear factors
pls explain
thanx in advance

Solve it as if it were a normal quadratic.