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Quadratic equation with complex coefficients

asked 2019-01-08 15:16:03 -0500

EvgenyM gravatar image

updated 2019-01-08 16:11:26 -0500

tmonteil gravatar image

How can I solve x^2 - (1 + I)*x + 6 + 3*I == 0 to get answers z = 3*I and z = 1 - 2*I ? When I enter

solve(x^2 - (1 + I)*x + 6 + 3*I == 0, x)

I get

[x == -1/2*sqrt(-10*I - 24) + 1/2*I + 1/2, x == 1/2*sqrt(-10*I - 24) + 1/2*I + 1/2]
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answered 2019-01-08 16:15:02 -0500

tmonteil gravatar image

The solutions are correct but they are not fully simplified.

sage: f= x^2 - (1 + I)*x + 6 + 3*I
sage: solve(f==0,x)
[x == -1/2*sqrt(-10*I - 24) + 1/2*I + 1/2, x == 1/2*sqrt(-10*I - 24) + 1/2*I + 1/2]

For each solution, you can simplify its right-hand-side as follows:

sage: [s.rhs().full_simplify() for s in solve(f==0,x)]
[3*I, -2*I + 1]
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Asked: 2019-01-08 15:16:03 -0500

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Last updated: Jan 08