Help converting complex number to cartesian

In summary, the conversation is about converting a dis equation to cartesian form, sketching it on an argand diagram, and finding complex numbers that satisfy a given relation. The solution involves replacing z with x+iy and manipulating the equation to find a relation between x and y, which can then be solved for either variable.
  • #1
meee
87
0
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:
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  • #2
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
ok... { x+yi: x + y = x*y }

like dat?
 
  • #4
meee said:
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.
 
  • #5
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
 
  • #6
meee said:
1/x + 1/y = 1
x + y = 1
What happens in this step?

I'd say:

[tex]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}}[/tex]
 
  • #7
howd u do that last step?
 
  • #8
meee said:
howd u do that last step?
That one isn't necessary, I split the fraction (by doing the division or manipulating the fraction):

[tex]
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}}
[/tex]
 
  • #9
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
meee said:
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 :smile:
 

1. What is a complex number?

A complex number is a number that is composed of both a real part and an imaginary part. It is typically written in the form a + bi, where a is the real part and bi is the imaginary part with i representing the imaginary unit.

2. How do I convert a complex number to cartesian form?

To convert a complex number to cartesian form, you simply need to separate the real and imaginary parts and write them in standard cartesian form as (a, b). For example, the complex number 3 + 4i would be written as (3, 4).

3. Can I convert a cartesian point to a complex number?

Yes, you can convert a cartesian point to a complex number by simply taking the x-coordinate as the real part and the y-coordinate as the imaginary part. For example, the cartesian point (3, -2) would be equivalent to the complex number 3 - 2i.

4. What is the purpose of converting to cartesian form?

Converting a complex number to cartesian form can be useful in visualizing and graphing complex numbers on the complex plane. It also allows for easier calculations and operations with complex numbers.

5. Are there any rules for converting complex numbers to cartesian form?

Yes, there are a few rules to keep in mind when converting complex numbers to cartesian form. The real part comes first, followed by the imaginary part. Also, be sure to use parentheses around the imaginary part to avoid confusion with multiplication.

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