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:

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