IB μαθηματικά HL – Complex Numbers

Complex Numbers, Quadratic over complex field – IB Mathematics HL

Solve the following quadratic equation in the complex numbers.

\(x^2-2x+2=0\)

Solution

The Discriminant of the above quadratic equation is

\(D=(-2)^2-4(2)=4-8=-4=4i^2\)

So the roots will be given by the following formula:

\(z_{1,2}= \frac{2\pm \sqrt{4i^2}}{2} \Rightarrow\) \(z_{1,2}= \frac{2 \pm (2i)}{2}\Rightarrow\) \(z_{1,2}= 1 \pm i \)