z^2+3iz+1=0

Solution for z^2+3iz+1=0 equation:

Simplifying
z2 + 3iz + 1 = 0

Reorder the terms:
1 + 3iz + z2 = 0

Solving
1 + 3iz + z2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + 3iz + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 3iz + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3iz + z2 = 0 + -1
3iz + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
3iz + z2 = -1

Add '-1z2' to each side of the equation.
3iz + z2 + -1z2 = -1 + -1z2

Combine like terms: z2 + -1z2 = 0
3iz + 0 = -1 + -1z2
3iz = -1 + -1z2

Divide each side by '3z'.
i = -0.3333333333z-1 + -0.3333333333z

Simplifying
i = -0.3333333333z-1 + -0.3333333333z