Question

Define complex roots.​

Answer 1

n general, a root is the value which makes polynomial or function as zero. Consider the polynomial, P (x) = a0xn + a1xn-1 + …+an-1x+an where ai ∈ C,i=1 to n and n ∈ N. Then, αi where i ∈ {1,2,3,…,n } is said to be a complex root of p(x) when αi ∈ C and p(αi)=0 for i ∈ {1,2,3,…,n }. In the quadratic equation ax2+bx+c=0, a, b, c are real numbers, the discriminant b2 –4ac< 0, then its roots are complex roots. Moreover, the complex number's form is a+ib, where a and b are real numbers.

Example:

Consider p(x)=x2 +1.

First, obtain the discriminant.

Therefore, the roots are complex roots.

Then, the roots are determined as follows:

Thus, the roots of p(x) is i,–i, which are complex roots. That is, p(i)=0 and p(–i)=0 with

i,–i ∈ C.

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