# Help converting complex number to cartesian

1. Mar 9, 2006

### meee

how convert dis to cartesian form!!?!
quation was here
and then i will need to sketch on an argand diagram.
help apreciated thnx

Last edited: Mar 9, 2006
2. Mar 9, 2006

### TD

I'm not sure what you mean, but how about replacing z with x+iy and then write out the equation in terms of x and y.

3. Mar 9, 2006

### meee

ok... { x+yi: x + y = x*y }

like dat?

4. Mar 9, 2006

### TD

Indeed, now you found a relation between x and y, the real and imaginary part. You can even solve this for either x or y. So you're looking for all the complex numbers which satisfy this relation.

5. Mar 9, 2006

### meee

yea i dont kno, don reli get it... cud i do dis?

and then divide by xy....
1/x + 1/y = 1

= x + y = 1

= x^2 + y^2 = 1

6. Mar 9, 2006

### TD

What happens in this step?

I'd say:

$$xy = x + y \Leftrightarrow xy - y = x \Leftrightarrow y\left( {x - 1} \right) = x \Leftrightarrow y = \frac{x}{{x - 1}} = 1 + \frac{1}{{x - 1}}$$

7. Mar 9, 2006

### meee

howd u do that last step?

8. Mar 9, 2006

### TD

That one isn't necessary, I split the fraction (by doing the division or manipulating the fraction):

$$y = \frac{x}{{x - 1}} = \frac{{x - 1 + 1}}{{x - 1}} = \frac{{x - 1}}{{x - 1}} + \frac{1}{{x - 1}} = 1 + \frac{1}{{x - 1}}$$

9. Mar 9, 2006

### meee

ahh ok... THANKYOU so much, i think it works... subing into the original equation... like 3+1.5 and 3*1.5 both = wooohopo thanks

10. Mar 9, 2006

### TD

You're welcome