IGCSE/GCSE/O & A Level/IB/University Student Forum
Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Monopoly on November 16, 2010, 01:30:58 pm
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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?
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The easiest method to solve this is to simply solve the quadtratic equation as it is is given.
Thus the roots are
and
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)
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The easiest method to solve this is to simply solve the quadtratic equation as it is is given.
Thus the roots are
and
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)
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One hour
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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
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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?
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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
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someone?
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:(
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When they say sketch they mean circle like, not an artist' drawing. A VERY ROUGH SKETCH
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Write the polynomial 9z² - 6z + 5 as a product of linear factors
pls explain
thanx in advance
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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.