write a quadratic equation with the given solutions.?

Question

i to the square root of 2, -i to the square root of 2

Answer 1

if an equation has a square root=a , you can divide it by (x-a)

so the equation is (x -i 2^0.5)(x -i2^0.5)

and knowing that (a-b) (a+b) = a^2+b^2

the equation is x^2 -2^0.5i^2 = x^2+2 since i^2 =-1

So x^2+2 =0