Author Topic: Complex number help  (Read 1718 times)

Offline Monopoly

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Complex number help
« 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 reitheta, giving the exact values of r and theta.

for the theta of reitheta, does the range -pie<theta=<pie still applies?

elemis

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Re: Complex number help
« Reply #1 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)

Offline Monopoly

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Re: Complex number help
« Reply #2 on: November 16, 2010, 03:30:09 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 2ei(2pie/3) & 2ei(4pie/3)
« Last Edit: November 16, 2010, 03:31:48 pm by Monopoly »

Offline astarmathsandphysics

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Re: Complex number help
« Reply #3 on: November 17, 2010, 08:46:32 am »
One hour

Offline astarmathsandphysics

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Re: Complex number help
« Reply #4 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

Offline Monopoly

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Re: Complex number help
« Reply #5 on: November 17, 2010, 11:10:18 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|eitheta is the polar form?

Offline Monopoly

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Re: Complex number help
« Reply #6 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

Offline Monopoly

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Re: Complex number help
« Reply #7 on: November 20, 2010, 06:26:12 am »
someone?

Offline Monopoly

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Re: Complex number help
« Reply #8 on: November 22, 2010, 05:51:38 pm »
  :(

Offline astarmathsandphysics

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Re: Complex number help
« Reply #9 on: November 23, 2010, 08:40:15 pm »
When they say sketch they mean circle like, not an artist' drawing. A VERY ROUGH SKETCH

Offline TJ-56

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Re: Complex number help
« Reply #10 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
« Last Edit: December 10, 2010, 09:04:11 pm by TJ-56 »

elemis

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Re: Complex number help
« Reply #11 on: December 22, 2010, 11:48:33 am »
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.