1+z+z^2+z^3+z^4+z^5+z^6+z^7+z^8+z^9=1-i

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Solution for 1+z+z^2+z^3+z^4+z^5+z^6+z^7+z^8+z^9=1-i equation: 


Simplifying
1 + z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = 1 + -1i

Add '-1' to each side of the equation.
1 + z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + -1 + z9 = 1 + -1 + -1i

Reorder the terms:
1 + -1 + z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = 1 + -1 + -1i

Combine like terms: 1 + -1 = 0
0 + z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = 1 + -1 + -1i
z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = 1 + -1 + -1i

Combine like terms: 1 + -1 = 0
z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = 0 + -1i
z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = -1i

Solving
z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = -1i

Solving for variable 'z'.

Reorder the terms:
i + z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = -1i + i

Combine like terms: -1i + i = 0
i + z + z2 + z3 + z4 + z5 + z6 + z7 + z8 + z9 = 0

The solution to this equation could not be determined.

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