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