# Equation with complex numbers

• Dec 6th 2010, 12:26 PM
Nforce
Equation with complex numbers
Solve the equation.

Attachment 19990

I don't know how to start and what to do here.

Maybe I start with inserting the square root of minus one, or changing Re(z) = 3, and Im(z) = 1.

I really don't know.

• Dec 6th 2010, 12:31 PM
tonio
Quote:

Originally Posted by Nforce
Solve the equation.

Attachment 19990

I don't know how to start and what to do here.

Maybe I start with inserting the square root of minus one, or changing Re(z) = 3, and Im(z) = 1.

I really don't know.

Write $z=x+iy\Longrightarrow Re(z)=x,\,Im(z)=y,\,\,\overline{z}=x-iy$ , and then compare real and imaginary parts in both sides.

Tonio
• Dec 6th 2010, 12:32 PM
TheEmptySet
Quote:

Originally Posted by Nforce
Solve the equation.

Attachment 19990

I don't know how to start and what to do here.

Maybe I start with inserting the square root of minus one, or changing Re(z) = 3, and Im(z) = 1.

I really don't know.

This should get you started any complex number $z$ can be written in the form

$z=x+iy$ then $\text{Re}(z)=x$ and $\text{Im}(z)=y$

and note that two complex numbers are equal if and only if there real and imaginary parts are equal. for example

$z=3+4i$ if and only if $x=3 \text{ and } y=4$

Try this and post again if you get stuck.
• Dec 6th 2010, 12:33 PM
Plato
That is just $(2xy)i=(x+3)+(-y+1)i.$
• Dec 6th 2010, 01:07 PM
Nforce
I still can't see what are we doing. All those x,y and i confused me. At the "standard" equation you just have one variable.
• Dec 6th 2010, 01:14 PM
Plato
Quote:

Originally Posted by Nforce
I still can't see what are we doing. All those x,y and i confused me. At the "standard" equation you just have one variable.

The long and short of this is: You are just not ready to tackle this question.
Have a sit down, face-to-face with your instructor.
• Dec 8th 2010, 12:39 AM
Nforce
Now I understand, I have just a linear equation, I need to find x, and y and then insert them back to see if left side is equal to right. And I have to set the real parts of equation to equal and same for imaginary part

Am I right?

I don't have an instructor, this forum is my instructor.
• Dec 8th 2010, 03:12 AM
Plato
Quote:

Originally Posted by Nforce
I don't have an instructor, this forum is my instructor.

That is a very bad idea.
In fact, it is a policy of the forum that we are not a homework service nor are we a tutorial service.
• Dec 9th 2010, 07:07 AM
Nforce
I apologize, but I understand now, thanks to this forum and you guys.