Write the quadratic that has real coefficients and complex solutions z1=1+i, z2=1-i.

The quadratic equation is: ax^2 + bx + c =
0

We could determine the real coefficients a,b,c, using
Viete's relations:

z1 + z2 =
-b/a

1 + i + 1  -i =
-b/a

We'll combine and eliminate like
terms:

2 = -b/a

z1*z2 =
c/a

(1+i)(1-i) = c/a

We'll
apply the formla of difference of squares:

1^2 - i^2 =
c/a

1^2 - (-1) = c/a

1 + 1 =
c/a

c/a = 2

The
quadratic equation is: x^2 - 2x + 2 = 0.