Complex Solutions to A "Complex" quadratic (1 Viewer)

[Ajihood]

Hey guys just wondering if you could help with this question as it is tearing my hair out. I have tried so many things and rearranged it so many times.

3(|z|)^2 + _z + 2z = 0

Where _z is conjugate of Z (No idea how to imput Z hat!)

The question say find all complex roots of it and gives a hint to "write z = x + iy in Cartesian form"

I know |z|^2 = z_z but i dont know what to do with it.

Thanks for any help.

 

[Trebla]

Hey guys just wondering if you could help with this question as it is tearing my hair out. I have tried so many things and rearranged it so many times.

3(|z|)^2 + _z + 2z = 0

Where _z is conjugate of Z (No idea how to imput Z hat!)

The question say find all complex roots of it and gives a hint to "write z = x + iy in Cartesian form"

I know |z|^2 = z_z but i dont know what to do with it.

Thanks for any help.

Letting z = x + iy
3(x² + y²) + x - iy + 2x + 2iy = 0
3x² + 3y² + 3x + iy = 0
Equating real and imaginary parts
y = 0 and
3x² + 3y² + 3x = 0
=> x² + y² + x = 0
But y = 0, hence
x² + x = 0
x = 0, - 1
This basically means that z must be a real number with z = 0, - 1 as solutions

 

[MC Squidge]

0+0i is a solution

and -1+0i

guy above made a mistake

 

[lolokay]

3x² + 3y² + 3x = 0
=> x² + y² + 3x = 0
But y = 0, hence
x² + 3x = 0
x = 0, - 3
This basically means that z must be a real number with z = 0, - 3 as solutions

do you mean x² + y² + x?
so z = 0, -1

 

[MC Squidge]

yes he does

 

[Ajihood]

Hey guys just wondering if you could help with this question as it is tearing my hair out. I have tried so many things and rearranged it so many times.

3(|z|)^2 + _z + 2z = 0

Where _z is conjugate of Z (No idea how to imput Z hat!)

The question say find all complex roots of it and gives a hint to "write z = x + iy in Cartesian form"

I know |z|^2 = z_z but i dont know what to do with it.

Thanks for any help.

Sorry guys I made a mistake in the imput of the question. There should be a square over the conjugate of z_

so the question is:

3(|z|)^2 + (_z)^2 + 2z = 0

where _z = conjugate of z

Sorry about that

 

[x.Exhaust.x]

All of the algebra and manipulation seems fine Timothy.Siu, but I can't grasp the part below:

when y=0 x=0
when x=1 y=+-root3i

i think.

What equation did you sub it back into?

 

[Timothy.Siu]

All of the algebra and manipulation seems fine Timothy.Siu, but I can't grasp the part below:



What equation did you sub it back into?

umm i made 2 equations, one by equating imaginaries and one by equating real.

 

[tommykins]

 

[tsukasu]

u noob Timothy.Siu

 

[lil-angeliz]

so is the final anwer 0+0i ans 1+- square root 3 ????

 

[Timothy.Siu]

so is the final anwer 0+0i ans 1+- square root 3 ????

no, its -1+0i, 0+0i

 

[Templar]

This is a MATH1001 assignment question. Try doing it yourself first.

Why are the first year students so eager to cheat and get other people to do their assignments this year...

 

[tommykins]

This is a MATH1001 assignment question. Try doing it yourself first.

Why are the first year students so eager to cheat and get other people to do their assignments this year...

hahah our yr is shit at uni, 09ers are shit at hsc.

 

[vds700]

hahah our yr is shit at uni, 09ers are shit at hsc.

hahahaha