# Homework Help: Exact Cartesian Form

1. Nov 4, 2007

### nk735

Hello,
My question comes in two parts, I don't know if the first part is relevent to the second so i'll put it in anyway.

a. Express 1 + root(3)i in polar form

I can solve this to get:

2cis(pi/3)

My problem is with part b.

b. Solve the quadratic equation z^2 + 2z - root(3)i = 0, expressing your answers in exact cartesian form

I used the quadratic formula (I don't like completing the square) to get:

z = (-2 + root(4 + 4root(3)i))/2 and z = (-2 -root(4 + 4root(3)i))/2

However, i'm lost with the 'exact cartesian form' part.

Any help would be appreciated, thanks.

Last edited: Nov 4, 2007
2. Nov 4, 2007

### Dick

I think cartesian form just means express the answer in the form a+bi. You now have to express the square roots of the complex quantities in that form. It might actually have been easier to complete the square.

3. Sep 3, 2009

### Awsom Guy

Ok I think You should get the real part and the imaginary part:
I think this is:
-2/2 and -2/2 are the reals.
Sqrt(4+4Sqrt3i)/2 and -Sqrt(4+4Sqrt3i)/2
Put these together and you should get a real part and an imaginary part.
I hope that helps. Don't take this as the real answer I might be wrong.