Quadratic equation with complex coefficients

You entered the following expression

Result of the solution of the set equation

It is known that quadratic equation:   has roots which are calculated on a simple forumula .

Online of decisions is a lot of, our boat, calculates a quadratic equation if its coefficients are complex numbers. 

It would be desirable to notice that not only complex numerical values, but also any complex expression can be coefficients of a quadratic equation. It undoubtedly expands possibilities of the presented service, and gives certain advantages. 

Well and it is natural, for those who well studied at school, and understanding that complex numbers it is only expanded representation of our "usual" real numbers, a conclusion follows that this service correctly considers and in case numbers in coefficients have the valid values.

In order that on the known roots it was possible to construct any equation including square with complex coefficients it is possible to use the Creation of a Polynom (Polynomial) of One Variable resource online 

Examples

We write coefficients to the entry field 

4 8-i -i

Do not forget that at least one gap divides these values the answer will be following 

You entered the following expression

Result of the solution of the set equation

We solve the complex equation: x^2 + (2-0.25i) *x + (0-0.25i) = 0 First root of the equation = - 0.0078432583508+0.125i Second root of the equation = - 1.9921567416492+0.125i

Here we see that coefficients are presented in the form of complex expressions,

but for the boat it is not a hindrance.

We write in inquiry

2-i ln (1+sin (i))-3

and we receive result 

You entered the following expression

Result of the solution of the set equation

We solve the complex equation: x^2 + (0.0003584355453+0.4330639593925i)*x + (-1.2-0.6i)= 0  First root of the equation = 1.1073006922543+0.0543883355731i  Second root of the equation = -1.1076591277997-0.4874522949657i