if one of a quadratic equation is 1/2-2i, what is the equation. the other root is 1/2+2I but i don't know how to find the equation

Answer 1

You can use the property that for any quadratic of the form
ax^2 + bx + c = 0
the sum of the roots is -b/a
the product of the roots is c/a

sum of the roots = 1/2 - 2i + 1/2 + 2i = 1
product of roots = (1/2 - 2i)(1/2 + 2i)
= 1/4 - 4i^2 = 1/4 + 4 = 17/4

equation:
x^2 - x + 17/4 = 0
4x^2 - 4x + 17 = 0