Question

2 square roots of _2 + 2(square root3)i

Answer 1

Let a+ib be the square root, then a²-b²+2iab=-2+2i√3.

Therefore, equating real and imaginary: ab=√3 and b=√3/a.

a²-b²=-2, a²-3/a²=-2, a⁴-3=-2a², a⁴+2a²-3=(a²+3)(a²-1)=(a²+3)(a-1)(a+1).

So a=±1 and b=±√3. The solutions are 1+i√3 and -1-i√3.