Complex number help

[Monopoly]

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?

[elemis]

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)

[Monopoly]

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 2e^i(2pie/3) & 2e^i(4pie/3)

[astarmathsandphysics]

One hour

[astarmathsandphysics]

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

[Monopoly]

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?

[Monopoly]

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

[Monopoly]

someone?

[Monopoly]

 

[astarmathsandphysics]

When they say sketch they mean circle like, not an artist' drawing. A VERY ROUGH SKETCH

[TJ-56]

Write the polynomial 9z² - 6z + 5 as a product of linear factors
pls explain
thanx in advance

[elemis]

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.