How do I solve this complex equation? Thanks!?

Determine all the solutions to following equation:

z^4-z^3+z-iz-i+1=0

i^2 = -1

one solution is z=1

Thanks!

1 Answer

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  • 7 years ago

    Actually, 1 is NOT a solution. Just substitute 1 into the expression to get

    1 - 1 + 1 -i -i + 1 = 2 -2i ≠ 0

    In fact, z =-1, or ±i are not solutions.

    Are you sure you wrote down the equation correctly? I tried Wolframalpha.com on the problem and it was able to find all 4 roots but they're all complex and messy.

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