## How to eliminate imaginary parts of complex expression?

Hi,
I have a problem on how to convert the imaginary parts of expression into all real parts. For example:

x1 = - (a + ib)
x2 = (a + ib)
x3 = - (a - ib)
x4 = (a - ib)

My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used Eulers Formula, De Moivers theorem, polar coordinates to solve this problem but still ending with imaginary parts.

 Quote by kaizen.moto Hi, I have a problem on how to convert the imaginary parts of expression into all real parts. For example: x1 = - (a + ib) x2 = (a + ib) x3 = - (a - ib) x4 = (a - ib) My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts. I have used Eulers Formula, De Moivers theorem, polar coordinates to solve this problem but still ending with imaginary parts. Please help me how to solve this problems. Many thanks in advance.
If I think what you're trying to do is find Re(z) where z is the complex variable using a formula, then the only way to find Re(z) without just getting it directly by looking at it, is to use the conjugate.

Re(z) = (z + conjugate(z))/2

If you have the polar coordinates you can simply use

Re(z) = r * cos(theta)

Hope that helps!

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 Quote by kaizen.moto Hi, I have a problem on how to convert the imaginary parts of expression into all real parts. For example: x1 = - (a + ib) x2 = (a + ib) x3 = - (a - ib) x4 = (a - ib)

My question is that how to express x1, x2, x3 and x4 in terms of real parts only without imaginary parts.[quote]
You can't. Because those are complex numbers, they cannot be expressed solely in terms of real numbers. If you mean "express only in terms of a, the real part of each number, you can't do that either because they all depend upon b, the imaginary part.

 I have used Eulers Formula, De Moivers theorem, polar coordinates to solve this problem but still ending with imaginary parts. Please help me how to solve this problems. Many thanks in advance.
It's not clear what you want to do- you can't write a complex number without using imaginary numbers.

## How to eliminate imaginary parts of complex expression?

As HallsofIvy said, you can't. You should be clearer with your word choice if you wish to do what chiro referred to.

As per your problem: take a look at the variables and see if you can find the conjugate of each expressed as another variable, and then consider their sum.

 Tags complex numbers, imaginary