What kind of equation is z^4-3z^2+2=0 ?

This equation is called biquadratic equation and it is
easy to solve.

This equation is reduced to a quadratic
equation when doing the substitution z^2 = x.

We'll
re-write the equation in x:

x^2 - 3x + 2 =
0

We'll apply quadratic
formula:

x1 = [3+
sqrt(9-8)]/2

x1 = (3+1)/2

x1 =
2

x2 = (3-1)/2

x2 =
1

But, we'll have to find
z1,z2,z3,z4.

z^2 = x1

z^2 =
2

z1 = sqrt 2 and z2 = -sqrt
2

z^2 = x2

z^2 =
1

z3 = -1 and z4 =
1

The solutions of the biquadratic equation
are: {-sqrt2 ; -1 ; 1 ; sqrt2}.