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.