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I need to find complex roots without a calculator (which wasn't helpful anyway). For x 4 +4 I know I can use the sum of

I need to find complex roots without a calculator (which wasn't helpful anyway).

For x⁴+4 I know I can use the sum of perfect squares to get (x2+2i)(x22i) , but then that would leave x=2i So how do I further decompose (x2+2i)(x22i) ?

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