z^2+(2+sqrt(-1))z+1=0

Solution for z^2+(2+sqrt(-1))z+1=0 equation:

Simplifying
z2 + (2 + sqrt(-1)) * z + 1 = 0

Reorder the terms for easier multiplication:
z2 + (2 + -1qrst) * z + 1 = 0

Reorder the terms for easier multiplication:
z2 + z(2 + -1qrst) + 1 = 0
z2 + (2 * z + -1qrst * z) + 1 = 0

Reorder the terms:
z2 + (-1qrstz + 2z) + 1 = 0
z2 + (-1qrstz + 2z) + 1 = 0

Reorder the terms:
1 + -1qrstz + 2z + z2 = 0

Solving
1 + -1qrstz + 2z + z2 = 0

Solving for variable 'q'.

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

Add '-1' to each side of the equation.
1 + -1qrstz + 2z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + -1qrstz + 2z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1qrstz + 2z + z2 = 0 + -1
-1qrstz + 2z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1qrstz + 2z + z2 = -1

Add '-2z' to each side of the equation.
-1qrstz + 2z + -2z + z2 = -1 + -2z

Combine like terms: 2z + -2z = 0
-1qrstz + 0 + z2 = -1 + -2z
-1qrstz + z2 = -1 + -2z

Add '-1z2' to each side of the equation.
-1qrstz + z2 + -1z2 = -1 + -2z + -1z2

Combine like terms: z2 + -1z2 = 0
-1qrstz + 0 = -1 + -2z + -1z2
-1qrstz = -1 + -2z + -1z2

Divide each side by '-1rstz'.
q = r-1s-1t-1z-1 + 2r-1s-1t-1 + r-1s-1t-1z

Simplifying
q = r-1s-1t-1z-1 + 2r-1s-1t-1 + r-1s-1t-1z

Reorder the terms:
q = 2r-1s-1t-1 + r-1s-1t-1z-1 + r-1s-1t-1z