Solve 4x^4=1-3x^2 for all complex roots

4x⁴ = 1 - 3x²

4x⁴ + 3x² - 1 = 0

Factor the left side:

(4x² - 1) (x² + 1) = 0

((2x)² - 1²) (x² - i ²) = 0

(2x + 1) (2x - 1) (x - i ) (x + i ) = 0

Then

2x + 1 = 0   or   2x - 1 = 0   or   x - i = 0   or   x + i = 0

Solve for x :

x = -1/2   or   x = 1/2   or   x = i   or   x = -i

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