explain the complex rootwhat is a complex root

2 Answers | Add Yours

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

The algebraic form of an imaginary root is `z = x + i*y` , where x represents the real part and y represents the imaginary part. A polynomial can only have an even number of comeplex roots since if there exists a complex root, hence there also exists its complex conjugate.

The following example shows a quadratic equation with two complex conjugate roots, such that:

`x^2 - 4x + 13 = 0`

Using quadratic formula yields:

`x_(1,2) = (4+-sqrt(16 - 52))/2 => x_(1,2) = (4+-sqrt-36)/2`

`x_(1,2) = (4+-6*i)/2 => x_1 = 2 + 2i; x_2 = 2 - 3*i`

Hence, as conclusion, if the problem allows, you may consider the real roots of a polynomial equation as complex, having the imaginary parts `y = 0` .

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Usually, a complex root comes in pairs. So, if an equation has a complex root, it has as root the conjugate of the complex root, too.

Let's say that z = a + bi is the complex root of an equation of n-th order. The equation will have as root the conjugate z' = a - bi, too.

For a quadratic, the complex roots eliminate the real roots.

The complex roots of the quadratic occur when the discriminant of the equation is negative.

We’ve answered 319,635 questions. We can answer yours, too.

Ask a question