Help converting complex number to cartesian

[meee]

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

 

[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.

 

[meee]

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

like dat?

 

[TD]

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

like dat?

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.

 

[meee]

yea i don't 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

 

[TD]

1/x + 1/y = 1
x + y = 1

What happens in this step?

I'd say:

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

 

[meee]

howd u do that last step?

 

[TD]

howd u do that last step?

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

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

 

[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

 

[TD]

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

You're welcome