Write a quadratic equation that has 5 + 2i as one of its roots.
Can someone show me a step by step method on solving the above problem.
The only way to make disappear such a complex number is to multiply by its conjugate.
Let $\displaystyle \bar{z}$ be the conjugate of z.
$\displaystyle (x-z)(x-\bar{z})=x^2-x(\underbrace{z+\bar{z}}_{\text{real number}})+\underbrace{z \cdot \bar{z}}_{\text{real number}}$
See why these are real numbers by noting that $\displaystyle z=a+ib$ (therefore, $\displaystyle \bar{z}=a-ib$)