This is FAO anyone who has a clue about complex numbers…

Got a maths problem:

Find the two roots of 2+2(root 3)i

Did it the usual way, using polar form [mod, arg]

got an answer of (±)(root 3)(±)i

The question then went on to say

‘now use the alternative method started below…marks will NOT be awarded for substituting into an equation’

Let a+bi be one of the roots

then (a+bi)^2 = 2+2(root 3)i

…

Here’s how far I managed to get:

a^2 + (2ab)i + b^2 i^2 = 2 +2(root3)i

therefore, equating real and imaginary parts:

a^2 -b^2 = 2

and

ab = root 3

after that, I’m at sea…thought about substituting into the quadratic but thought that that would be in violation of the question…

Any mathdopers out there in the teeming millions able to ease my pain?