Roots of unity (1 Viewer)

[ashokkumar]

Find the solution to the following equation. Express answer in a + bi form.

x^2 + (3 - i)x - 3i = 0

 

[shaon0]

Find the solution to the following equation. Express answer in a + bi form.

x^2 + (3 - i)x - 3i = 0

x^2+3x-ix-3i=0
x(x+3)-i(x+3)=0
(x+3)(x-i)=0
x=-3,i

 

[ashokkumar]

can this be solved using roots of unity?

 

[xV1P3R]

Aren't roots of unity nth roots of 1 and hence not applicable to this question?
ie z^n - 1 = 0

 

[addikaye03]

x^2+3x-ix-3i=0
x(x+3)-i(x+3)=0
(x+3)(x-i)=0
x=-3,i

Shit, that's nice. I wouldn't have seen that lol I would have done the whole: Discriminant=>sqaure root of a+ib => Quadratic formula LOL noob.

 

[h3ll h0und]

i think u cud also equate real and imaginary parts but the way shaon did it was quick and id definitely miss that in an exam.

 

[shaon0]

Shit, that's nice. I wouldn't have seen that lol I would have done the whole: Discriminant=>sqaure root of a+ib => Quadratic formula LOL noob.

I always look out for the little things. Just needed to realise the 1 and -3 coeffs and its easy from there.