What are complex roots??

• Complex numbers?provide solutions for quadratic equations which have?no real roots

• Complex roots occur when solving a quadratic with a?negative discriminant
  • This leads to square rooting a negative number

How do we solve a quadratic equation with complex roots?

• We solve an equation with complex roots in the same way we solve any other quadratic equations
  • If in the form ?we can?rearrange?to solve
  • If in the form ?we can?complete the square?or use the?quadratic formula
• We use the property ?along with a manipulation of surds

• When?the?coefficients?of the quadratic equation are?real, complex roots occur in?complex conjugate?pairs
  • If is a root of a quadratic with real coefficients then?is also a root
• When the coefficients of the quadratic equation are?non-real, the solutions will?not?be complex conjugates
  • To solve these use the quadratic formula

How do we find a quadratic equation given a complex root?

• We can find the equation of the form ?if you are given a complex root in the form
  • We know that the complex conjugate ?is another root,
  • This means that andare?factors?of the quadratic equation
  • Therefore
    • Writing this as?will speed up expanding
  • Expanding?and?simplifying?gives us a quadratic equation where b and c?are?real?numbers