# Polar coordinate

1. ### teng125

416
x^2 + 2x + 5 = 0.Find the root of this eqn.can use polar system.

pls help.......
thanx....

2. ### StatusX

2,567
That answer is in cartesian form. A polar answer looks like r e. Polar coordinates wouldn't really be appropriate to do this problem, although you could easily put the final answer from cartesian form, z=a+bi, into polar coordinates using r2=a2+b2, Θ=tan-1(b/a).

Last edited: Jan 12, 2006
3. ### teng125

416
can youpls show me the stpes??plsssss

4. ### StatusX

2,567
I won't do it for you, but I'll answer any specific questions you have. But if you are going to use cartesion coordinates, just use the quadratic formula.

5. ### teng125

416
i have tried it.so is it the ans is 5^1/2 e(j0.6476pai)??

6. ### HallsofIvy

40,543
Staff Emeritus
Please copy the problem exactly as it is given to you. In your first post you said
"x^2 + 2x + 5 = 0.Find the root of this eqn.can use polar system.

"can use polar system" doesn't mean you have to! It's easy to solve the equation by completing the square. Yes, the solutions are
x= -1+ 2i and x= -1- 2i. Are you required to write the answers in polar form?

7. ### aalmighty

17
AFAIK, there's no polar equivalent to adding numbers, so If anyone who knows how to solve it using polar system, please let us know.

Apart from that, it most prolly is to find the roots using quadratic formula in cartesian form ( x+iy ) and convert it to polar form

r(e)^iD, where r=sqrt(x^2+y^2) and angle D=arctan(y/x)

8. ### teng125

416
ya,require.....

9. ### aalmighty

17
then convert using the expressions I gave in the last post.

10. ### HallsofIvy

40,543
Staff Emeritus
Polar form of the number a+ bi is either $r(cos\theta+ i sin\theta)$ or $r e^{i\theta}$ (since $e^{i \theta}= cos\theta+ i sin\theta$ they are equivalent) where r is |a+ bi| and $\theta$ is the "argument" or angle the line through (0,0) and (a,b) makes with the positive real axis. For a+ bi, $r= \sqrt{a^2+ b^2}$ and $\theta= arctan(\frac{b}{a})$ as long as a is not 0. If a is 0 and b is positive, then $\theta= \frac{\pi}{2}$. If a is 0 and b is negative, then $\theta= -\frac{\pi}{2}$. The number 0 (0+ 0i) cannot be written in "polar form".

If you were given a problem requiring the answer in polar form, surely you were already taught all of that?