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Hey everyone! Here I have a problem I don't know how to solve so help would be greatly appreciated!

Here is an equation z^3+az^2+bz+c where a, b and c are real numbers. If the roots are drawn in the complex plane they form a triangle with area of 9 units. One root of the equation is 1+3i.

(a) Find other roots of the equation.

(b) Find a, b and c

The only thing I know is that if 1+3i is a root than 1-3i is also a root but more I don't know, I have no idea how to solve this without a, b and c i don't know how to find them.

-Thanks in advance!

EDIT: I think I finally figured out how to solve this. I tried to insert (1+3i) and (1-3i) into the equation and got a=1, b=4 and c=30 then I put it in the original equation and get the third root, z=-3. Is that correct? What is confusing me is that the area has to be 9, I don't get that.

## Homework Statement

Here is an equation z^3+az^2+bz+c where a, b and c are real numbers. If the roots are drawn in the complex plane they form a triangle with area of 9 units. One root of the equation is 1+3i.

(a) Find other roots of the equation.

(b) Find a, b and c

**2. The attempt at a solution**The only thing I know is that if 1+3i is a root than 1-3i is also a root but more I don't know, I have no idea how to solve this without a, b and c i don't know how to find them.

-Thanks in advance!

EDIT: I think I finally figured out how to solve this. I tried to insert (1+3i) and (1-3i) into the equation and got a=1, b=4 and c=30 then I put it in the original equation and get the third root, z=-3. Is that correct? What is confusing me is that the area has to be 9, I don't get that.

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