complex number question (1 Viewer)

[Hikari Clover]

find all complex solutions to the equation

i believe this is a easy question however i got stuck with this bit:mad1:

thx everyone

 

[tommykins]

cbf correcting

 

[youngminii]

Whenever you're stuck just sub in z = x + iy (or rcistheta)
So, 3[sqrt(x^2 + y^2)]^2 + (x - iy)^2 + 2(x + iy) = 0
3x^2 + 3y^2 + x^2 - y^2 - 2xyi + 2x + 2yi = 0
(2x^2 + y^2 + x) + (y - xy)i = 0
Equating Re & Im parts
2x^2 + y^2 + x = 0........ (1)
y - xy = 0
y(1 - x) = 0
Therefore y = 0 or x = 1
If y = 0 -> (1)
2x^2 + x = 0
x(2x + 1) = 0
x = 0 or -1/2
If x = 1 -> (1)
y^2 = -3
y = +=isqrt3
Therefore the solutions to the equation are z = 0, -1/2, 1 + isqrt3, 1 - isqrt3

Tommy, you made a mistake when you expanded (x - iy)^2
Also your -2ixy became 2ixy at the second last line
Few months after Year 12 and your 4U skills are already deteriorating

Edit: Lulz @ post above

 

[tommykins]

shhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.

im finding it hard to get back into correct algebraic shortcuts. haha

 

[waxwing]

y^2 = -3
y = +=isqrt3
Therefore the solutions to the equation are z = 0, -1/2, 1 + isqrt3, 1 - isqrt3

This step is not correct; in writing z = x+ iy we assume y to be a real number, therefore y^2 = -3 has no solutions. You can easily verify this by substituting 1 + iroot3 into the original equation. Your first two solutions were correct, of course.

 

[youngminii]

Oh shnap, I fail.

 

[GUSSSSSSSSSSSSS]

i fink quickest way is to change the modulus^2 to z.z(conjugate)

and also change z(conjugate)^2
to z.z(conjugate)

then ya factorise

and ya answer found in like 3 lines!

 

[youngminii]

Ye but many people (like me) can't remember those little identities.

 

[GUSSSSSSSSSSSSS]

yea learnin them is a bitch lol

but the one i used u use all the time when expanding factors in conjugate pairs
so like that one i rekon most ppl would remember

(but then i think its like the only one i remember too lol)

 

[Trebla]

i fink quickest way is to change the modulus^2 to z.z(conjugate)

and also change z(conjugate)^2
to z.z(conjugate)

then ya factorise

and ya answer found in like 3 lines!

z(conjugate)^2 is NOT equal to z.z(conjugate)

 

[GUSSSSSSSSSSSSS]

z(conjugate)^2 is NOT equal to z.z(conjugate)

eh lol ur rite

meh i too tired lol